RATIOS - SCALING
Math for Physics
( lab height of tree, old lab) lab3 (ratio surface/volume I )
lab4 (ratio surface/volume II ) lab5 (scaling and maps) lab6 sponge bob (scaling) lab 2 number PI lab 1scale (world history in 24hours)
PART1: RATIOS - connection to Chemistry
In Sciences (Physics, bio or Chem) finding the ratio between 2 quantities is an important tool. It allows you to investigate the relationship between 2 quantities and to compare them. Here some simple problems involving ratios:
1) ptable.com has the periodic table
A) Students are asked to find the mass of 1 penny and 1 quarter using a plate scale in the Chemistry lab.
They find 1 penny weighs m=2.5 g and the quarter M=5.7g . Find the ratio between these masses . M/m = __________
that means the quarter weighs ___________ times more than the penny.
They then weighs 20 pennies m1= __________, they weighs 20 quarters M1=________--, the ratio M/m= ____________.
The ratio comes out to be the ____________.
2)A) 1 mole is a unit of measurement used in Chemistry . 1 mole contains 6.02 1023 atoms (or molecules). This is called Avogadro number.
is that about million of million of particle ? billion of billion ? trillion of trillion ?
write this number in standard notation: _____________________________________________________________________
If you take a mole of sands, it will cover Los Angeles ___________ deep. (6m ? 60m? 600 m ? 1 meter = about 1 yard about 3 feet )
(just take a guess) A mole is a unit of measurement like a dozen. A dozen of apples contains _________ apples
but a mole of apples contains ___________ apples.
You can cover the EArh with 1 mole of marbles, up to 50 miles !
B) THe same principle of relative weighs applies also to the molecular world. (Chemistry). You can't weigh single molecules or atoms
but you can weigh several of them and work out the relative weighs of different element.
Suppose you weigh 1 mole of pure carbon (powder) (coal, diamonds, or your pencil tip is mostly carbon) and find 12g.
(the mass of a mole of an element is the atomic mass expressed in grams, you will find it in the periodic table)
1 mole of oxygen is 16g. The ratio between the mass of an atom of oxygen and the mass of an atom of carbon is therefore _________.
The oxygen atom weighs ___________ more than the carbon atom.
1 mole of hydrogen weighs 1g so 1 mole of molecules of water H2O weighs __________g (2 hydrogen and 1 oxygen)
(hint: water is H2O , so add up the atomic masses of 2 hydrogens and 1 oxygen)
Find the ratio of mass of an uranium atom and a hydrogen atom _________. Uranium is a very massive atom, unstable and radioactive.
It will spontaneously decay into smaller atoms producing in the process radioactive rays,
(hint : find ration between their atomic masses)
C) 1 penny is 1.55mm high. convert to meters (use Scientific notation). = ___________m convert to km _______________km.
1 mole of pennies (stacked up ) will be _____________ km high
hint: 1 mole is 6.02 1023
CAn you reach the moon with this pile ? (the moon is 385,000 km from Earth)
1 pile = ____________ times the distance of Earth-moon
CAn we reach the closest star ? (about 4 light years away and 1 light year = 1013km ) How many round trips ?
3)
A)
1 mole of nitrogen N is ______ g but 1 mole of N2 ( a gas made o 2 atoms of N) is __________g. (N2 = N + N , add the atomic mass)
(nitrogen gas is N2 and makes up 80% of air we breath )
1 mole of Cl is __________g but 1 mole of Cl2 (2 atoms of Cl) weighs __________g (Cl2 is made of 2 Cl = Cl + Cl attached to each other)
1 mole of H is _________g, 1 mole of Cl is _____________ g , but 1 mole of HCl is ___________g (HCl is H+Cl)
1 mole of oxygen O weighs ________g but 1 mole of the gas oxygen O2 weighs _________g ( O2 is O+O, it is a molecule )
(O2 make up 20% of the air we breath)
B) An understanding of ratios and relative weighs is essential in Chemistry. Specially when working with reactions.
Take this reaction for example: H2 + Cl2 = 2 HCL
That means 1 mole of H2 reacts with ________ mole of Cl2 to produce ___2 moles __ of HCL
Now use what you found in 3 A) !!! please understand what you did in 3A) !!! READ !
_________ g of H2 reacts with ____________g of Cl2 to produce _________g of HCL
( 1mole H2 in g) (1 mole of Cl2 in g ) (2 moles of HCL in g )
Using relative weighs (proportions) 100g of hydrogen will produce ___________ g of HCL (use the yellow line above)
hint: use the previous relative weighs in grams. set your proportion.
You will need _______ g of Cl2
In a chemical reactions, reactants react in a simple whole number ratio. (found by DAlton)
4) Using the mass of moles of particles, you can count by weighing. If you weighs 60g of carbon, you have ____ moles of carbons.
(1 mole of carbon is 12g). hint: 12g is 1 mole si 60 g is _______ moles ((proportions)
that is ____________ atoms of carbons.
(hint : use Avogadro number 1 mole = 12 g =6.02 1023 atoms so ........... proportion to solve)
If you weigh 100g of hydrogen gas (H2) you have __________ moles. hint: 1 mole of H2 = 2g
or _________ molecules of H2.
(hint: use Avogadro number 1 mole = 6.02 1023 molecules H2 so ... )
5)
A) 1 mole of H2 (hydrogen gas) = ________ g , 1 mole of N2 (nitrogen gas)= __________g, 1 mole of NH3 (ammonia) = __________ g (N + H + H + H)
B) Ammonia is an important chemical used for fertilizer. we know how to synthesize ammonia:
N2 + 3H2 = 2 NH3
1 mole of nitrogen gas reacts with __3____ moles of hydrogen gas to produce _________ moles of ammonia
So ______g of N2 reacts with _________ g of H2 to produce __________ g of NH3
( H2 in g ) (3 x N2 in g) (2 x NH3 in g )
(here is a cool website to practice balancing equations)
You get H2 from burning natural gas, N2 comes from the air. (20% oxygen and 80% nitrogen)
story:
The German chemist Fritz Haber is the one who discovered the making of ammonia in 1909. He gave Germany
an agriculture independence as the country didn't rely any more on South America to get Ammonia.
During world war I, by patriotism, he developed poisonous gas like chlorine. He is considered as the father
of chemical warfare. Haber was jewish and when the nazis came to power he was just
the jew Haber. He was exiled and died from heart attack in England. During the 1920s, scientists working at his institute developed
the cyanide gas formulation Zyklon B, which was used as an insecticide, especially as a fumigant in grain stores,
and also later, after he left the program, in the Nazi extermination camps, killing other Jews, including, with terrible irony, many of his relatives.
(source: wikipdia.org)
-----------------------------------------------------
7) The density of alcohol is 0.8g/ml. What is the weight of 50ml of alcohol ?
hint: 0.8g/ml means 0.8g for 1 ml. proportion again
8) The density of concentrated sulfuric acid is 1.85g/ml. What volume of the acid would weigh 74 g ?
hint: 1 ml = 1.85g so ...
9) One kilogram of metallic osmium, the heaviest substance known(atomic number is 76g), occupies a volume of 44.5 cm3. Calculate the density of osmium in grams
per cm3 (that is find the mass for 1 cm3 ). (hint; convert kg to g first, then set your proportion)
It is the densest natural element. Osmium is found in nature as an alloy, mostly in platinum ores
10) If the dot under a question mark (made with pencil) has a mass of 10-6g (micrograms), and you assume it is carbon, how many atoms are required to make
such a dot ?
hint: 1 mole of carbon is 12g and contains 6.02 1023 atoms so 10-6 g contains ..
11)
A) 1 mole of water H20 weighs _________ g ( H + H + O)
What is the approximate number of molecules in a drop of water which weighs 0.09g ?set your proportion
. 1 mole of water = _____ g (see A) and contains 6.02 1023 molecules H20 .so 0.09g contains ....... H20
12)
Consider the chemical reaction Mg + 2HCL = H2 + MgCL2
Magnesium (solid) reacts with Hydrogen chlorine (liquid) to produce hydrogen gas and magnesium chlorine.
A) mole of magnesium is _________g , 1 mole of HCL is __________g ( H + Cl), 1 mole of MgCl2 is _______g (Mg + Cl + Cl)
B) the formula shows that 1 mole of Mg reacts with _____ moles of HCL to produce _____ moles of hydrogen gas and ______ moles of MgCl2
so __________g of Mg reacts with __________g of HCL (2 moles of HCL) to produce _________g of H2 and ________ g of MgCl2
C)) 100g of Mg react with ______ g of HCL to produce _________ g of MgCl2
(proportion, use B)
13) (source) of the following problems:
A) 1.77 x 1028 atoms Cu = ___ mole Cu
= ___ grams Cu
B) 1.99 x 1025 molecules of H2O = ___ moles H2O
C) 0.667 moles Li = ___ g Li
D) 15.0 x 1023 atoms Zn = ___ g Zn
E) 4.75 x 106 atoms Al = ___ g Al
14)
A) what is 1 mole ?
B) define molar mass
C) state Avogadro number
15)
A) 0.250 mole Br = ___ atoms Br
B) 7.25 g Cu = ___ atoms Cu
16) fill the blanks
more problems (source)
16) REVIEW order of magnitude.
Consider the carbon atom. (average atom) with 12 nucleons inside.
If the atom (electronic cloud) is scaled up to a new year ball (about 1 m diameter)
a nucleon (proton or neutron) inside the nucleus would be the size of a human hair (about 20 micrometer diameter).
What is the order of magnitude ? (find the ratio between the ball's diameter and the hair diameter) _____ : 1 (in scientific notation)
That means the whole atom (nucleus + clouds of electrons) is ____________ times larger than the nucleon.
In a carbon you have ____ nucleons so the diameter of the nucleus is about ________ times smaller than the, whole atom.
17) if a nucleus is the size of a soccer ball (about 20cm across) the electronic cloud would be 9.5 miles away.
find the ratio between the size of the atom (9.5 miles) and the size of a nucleus (10cm).
Do you get about the same order of magnitude than before? (you need to convert miles to meter and cm to meter first)
18) REVIEW
10 trillion cells in our body = _____________ in scientific notation.
Each cell harbors 10 microbs. So ___________ (scientific notation) inhabit us.
If you take all our DNA strings, strtch them out and connect them you will
make 8000 round trips to the moon. How long is that in km (scientific notation) __________ km
(distance to the mooon, see problem 2)
PART2: ENVIRONMENT / ALTERNATIVE ENERGY
1) It is estimated that 2 105 tons of sulfur dioxide, SO2, enters the atmosphere daily owing to the burning of coal and petroleum products.
Assuming an even, distribution of the sulfur dioxide throughout the atmosphere , calculate in parts per million by weights the concentration
of SO2 added daily to the atmosphere. The weight of the atmosphere is 4.5 1015 tons.
hint: it is a proportion if: 2 105 is for 4.5 1015 then X is for 1 million
It takes about 40 days for the removal of acid sulfuric by rain. (acid rain that destroys trees and contaminates lakes )
2) source: Mathematics teaching in the middle school / Vol. 15 , No2, September 2009
Ethanol is now used as an alternative fuel. It is made from corns.
A) To measure the quantity of corns, farmer use a unit of mass called a bushel. 1 bushel is 56 pounds.
1 acre of corn field yields 150.7 bushels of corns. How many bushels can be produced on 300 acres ?
1000 acres ? Keep these numbers, you will need them for the coming questions.
(hint: set your proportion )
B) Only 15% of the corn produced is sent to an ethanol rafinery.
How many bushels are sent to rafinery from the corns grown on a 300 acres ?
1000 acres ?
(hint: proportion again 15 out of 100 is sent to rafinery . so use A) )
C) From each bushel, an thanol rafinery can produce 2.8 gallons of enthanol .
Using the numbers found in B) find the gallons of enthanol produced from the
corns grown from a 300 acres and from a 1000 acres
D) in 2008 9 billion gallons of ethanol was produced from rafineries.
Aprroximatly, how many bushels of corn were used in ethanol production?
(hint: use 1 bushel produces 2.8 gal )
PART 4: more problems ratio
1) REVIEW
0.0342 mm = ___________micrometers 0.00432 m = ________mm = _________ micrometers
4,232 micrometers = __________mm 2,000,000 micrometers = _________ m
4,232g = ________ kg 0.32 kg = ________g 3 tons = __________ kg
3,300 km = _________m 10-10 meters = _________ micrometers 10-2 meters = ________ mm
3.4 104 g = _________kg
2) REVIEW (in scientific notation)
1 billionth meter = _________ m 1 millionth meter = ____________m 1 thousandth gram= __________ g
20 million of million = _______________ 30 billion of billion = _____________ 1 hundredth = _________
1000 billion of molecules of proteins __________________.
3) a healthy person drinks 2 kg of water, eats 8kg of food and inhales 16 kg of air (only 20% of it is oxygen).
Whats is the ratio of weighs of air inhaled vs food eaten ?
4) The movie Austin Powers features Dr. Evil and his clone Mini Me. Mini Me is much smaller even if identical to Dr. Evil. Mini Me (in the movie) is said to me 1/8 of Dr Devil's size. Let's find out if this makes sense.
If Mini Me is 32 inches and 1/8 of Dr. Evil, how tall is Dr. Evil (in inches) ? Does this make sense ?
hint: the scale (ratio) is 1 inch (Mini ME) to 8 inches (Dr. evil). 1 foot = 12inches
5) In 2004, the population density (number of people per unit area) of the united states reached 80 people per square mile. How many people would you expect around Lake Wobegon, Minnesota, an area of 50 square miles?
hint: you are looking for people per square miles so divide people per square miles !
6) One of the MOST densely populated cities in Macao (a Chinese territory under Portuguese administration) with about 446,250 inhabitants living on 21 square kilometers of land. What is the population density per square kilometer in Macaw ? (that is the number of people per square kilometers) (hint: divide people by area)
hint: people per square kilometer. you divide.
7) According to Plato's description, the population of the lost city of Atlantis was between 6 and 10 millions people. If the area of Atlantis was 86,400 square kilometers and he population is assumed to have been 8,640,000 inhabitants, what was the population density for Atlantis (in people/km2) ?
8) Another densely population city is Monaco with 31,980 inhabitants living on 1.95 square kilometers of land. What is the population density per square kilometer in Monaco ?
9) A student is paid at the rate of $38 for 8 hours of work. What is the rate per hour?
hint: rate per hour means $ per hour so divide $ per hour !
10) Which is the fastest-growing plant you know ? A bamboo grew 36 inches in a 24 hour period. What was the hourly growth rate for this plant (in inches per hour that is in/hr)
That means: In every hour, the plant grows ____________, in 3 hours it grows ___________, in 1 day __________
hint: 1 day = 24 hours
11) The fruit with the lowest caloric value is the cucumber. A 11/2 pound cucumber as 109.5 calories. What is the caloric rate per pound of cucumbers ?
hint: that is calories per pound cal/lbs, remember: 11/2 = 1.5
12) A burger king hamburger has 275 calories and weighs 110 grams. Find the number of calories per gram.
13) THe fruit with the highest caloric value is the avocado: 1 1/2 pounds of edible avocado contain 1110 calories.
What is the caloric rate per edible pound ?
14) The air distance between New york and DAllas is 1375 miles. If a plane takes 21/2 hours to make the flight, what is the planet's rate of travel ? The rate represent the _____________ of the plane. (look at the units)
hint: Find the number miles traveled per hour . 2 1/2 = 2.50. Divide miles per hour. units = mph
15) One of the fastest marathon runners is Balaine Desimo, who completed 26 miles in 2.1 hours. TO the nearest mile, what was his rate of travel ?
hint: that is, find his speed = miles per hour =- miles/hours
16) elephants eat more than 1400 pounds of food a week How many pounds of food per day is that ?
hint: pounds per day. there are 7 days in a week
17) An AMerican alligator lives about 40 years and, during that time, grows about 3000 teeth, How many teeth per year is that ?
18) A Llama can travel 60 miles in three days. How many miles per day ?
19) you take a Microsoft Windows Professional class. It costs $698 for 21 hours. Find the cost per hour ?
20) A rhinoceros beetle weighs 30 grams and can carry 850 times its body weight, that is 25,500 grams. If a person could carry proportionally as much as the rhinoceros beetle, how much could a 60 kg student carry.(1 kg = 2.2 lbs)
hint: if you were are strong as that bug, you would be able to carry 850 times your mass (60kg). then convert to pounds.
21) A leaf-cutting ant weighting 1.5 grams can carry a leaf weighting 4.5 grams. If a person could proportionally carry as much weight, how much could a 60kg student carry?
hint: Find how many times (X) its body mass, the ant , can carry first. (4.5 / 1.5) = X. If the student is as strong , he would be able to carry also X times his mass.
Then convert kg to lbs.\
22) In the lab about ratios, you investigated the ratio between surface area versus volume. you found out that smaller objects have more? less ? area per unit mass than larger objects.
Scaling affects living organism. In the case of mammals, for example, size affects the life span of an organism. Small mammals live fast? slow ? and die young. Larger animals live at a leisurely pace and live __________.
23) Explain why if you were to scale up an moose to the size of an elephant, this animal would collapse.
(hint: the weight depends on the volume but the strength depends on the cross-sections of the limbs )
Fill the blank: As an animal gets larger it gets heavier but not ____________.
24) Find the product. Give the answer with the appropriate unit of measure.
I write fraction using slash. So one-third is 1/3, one half is 1/2, three-fifth is 4/5 ... you get it.
A) (3.5 hours) x 45 miles/1hour = ________ ______.
B) (500 dollars) x 12.2 schillings/1 dollar =
C) 3 dollars/1 square foot x (1222 square feet) =
D) (12 seconds) x 254feet /1 second = E)
E) (7meters/1minute) (60 minutes)
F) (168 hours/ 1 week) (52 weeks)
G) (3yards/1second) (12 seconds) - 10 yards
H) (15dollars / 1hour ) ( 8 hours) + 45 dollars
25) Monique uses 1.5 pounds of fertilizer for every 200 square feet of lawn. How many pounds of fertilizer will she have to use on a lawn that measured 3000 square feet?
26) In 10 years , the price of a scientific calculator went from $50 to $10. What is the ratio, as a fraction in simplest form, of the decrease in price to the original price?
27)
THe speed a boat travels is usually measured in nautical miles or knots. The Golden Gate-Sausalito ferry in California, which provides service between Sausalito and San Francisco, can travel at 20.5 knots. Find the speed in miles per hour. (1 knot = 1.15 miles per hour).
28) THe amounts of water typically used for common household tasks are given in the table below.
Find the number of liters needed for each task. (1 gallon = 3.79 liters)
29) Lake Baikal, in Siberia, is so large that it would take all the rivers on Earth combined an entire year to fill it.
At 1.62 km deep, it is the deepest lake in the world. Find the depth of Lake Baikal in miles. (1mile = 1.6 km).
In Sciences (Physics, bio or Chem) finding the ratio between 2 quantities is an important tool. It allows you to investigate the relationship between 2 quantities and to compare them. Here some simple problems involving ratios:
1) ptable.com has the periodic table
A) Students are asked to find the mass of 1 penny and 1 quarter using a plate scale in the Chemistry lab.
They find 1 penny weighs m=2.5 g and the quarter M=5.7g . Find the ratio between these masses . M/m = __________
that means the quarter weighs ___________ times more than the penny.
They then weighs 20 pennies m1= __________, they weighs 20 quarters M1=________--, the ratio M/m= ____________.
The ratio comes out to be the ____________.
2)A) 1 mole is a unit of measurement used in Chemistry . 1 mole contains 6.02 1023 atoms (or molecules). This is called Avogadro number.
is that about million of million of particle ? billion of billion ? trillion of trillion ?
write this number in standard notation: _____________________________________________________________________
If you take a mole of sands, it will cover Los Angeles ___________ deep. (6m ? 60m? 600 m ? 1 meter = about 1 yard about 3 feet )
(just take a guess) A mole is a unit of measurement like a dozen. A dozen of apples contains _________ apples
but a mole of apples contains ___________ apples.
You can cover the EArh with 1 mole of marbles, up to 50 miles !
B) THe same principle of relative weighs applies also to the molecular world. (Chemistry). You can't weigh single molecules or atoms
but you can weigh several of them and work out the relative weighs of different element.
Suppose you weigh 1 mole of pure carbon (powder) (coal, diamonds, or your pencil tip is mostly carbon) and find 12g.
(the mass of a mole of an element is the atomic mass expressed in grams, you will find it in the periodic table)
1 mole of oxygen is 16g. The ratio between the mass of an atom of oxygen and the mass of an atom of carbon is therefore _________.
The oxygen atom weighs ___________ more than the carbon atom.
1 mole of hydrogen weighs 1g so 1 mole of molecules of water H2O weighs __________g (2 hydrogen and 1 oxygen)
(hint: water is H2O , so add up the atomic masses of 2 hydrogens and 1 oxygen)
Find the ratio of mass of an uranium atom and a hydrogen atom _________. Uranium is a very massive atom, unstable and radioactive.
It will spontaneously decay into smaller atoms producing in the process radioactive rays,
(hint : find ration between their atomic masses)
C) 1 penny is 1.55mm high. convert to meters (use Scientific notation). = ___________m convert to km _______________km.
1 mole of pennies (stacked up ) will be _____________ km high
hint: 1 mole is 6.02 1023
CAn you reach the moon with this pile ? (the moon is 385,000 km from Earth)
1 pile = ____________ times the distance of Earth-moon
CAn we reach the closest star ? (about 4 light years away and 1 light year = 1013km ) How many round trips ?
3)
A)
1 mole of nitrogen N is ______ g but 1 mole of N2 ( a gas made o 2 atoms of N) is __________g. (N2 = N + N , add the atomic mass)
(nitrogen gas is N2 and makes up 80% of air we breath )
1 mole of Cl is __________g but 1 mole of Cl2 (2 atoms of Cl) weighs __________g (Cl2 is made of 2 Cl = Cl + Cl attached to each other)
1 mole of H is _________g, 1 mole of Cl is _____________ g , but 1 mole of HCl is ___________g (HCl is H+Cl)
1 mole of oxygen O weighs ________g but 1 mole of the gas oxygen O2 weighs _________g ( O2 is O+O, it is a molecule )
(O2 make up 20% of the air we breath)
B) An understanding of ratios and relative weighs is essential in Chemistry. Specially when working with reactions.
Take this reaction for example: H2 + Cl2 = 2 HCL
That means 1 mole of H2 reacts with ________ mole of Cl2 to produce ___2 moles __ of HCL
Now use what you found in 3 A) !!! please understand what you did in 3A) !!! READ !
_________ g of H2 reacts with ____________g of Cl2 to produce _________g of HCL
( 1mole H2 in g) (1 mole of Cl2 in g ) (2 moles of HCL in g )
Using relative weighs (proportions) 100g of hydrogen will produce ___________ g of HCL (use the yellow line above)
hint: use the previous relative weighs in grams. set your proportion.
You will need _______ g of Cl2
In a chemical reactions, reactants react in a simple whole number ratio. (found by DAlton)
4) Using the mass of moles of particles, you can count by weighing. If you weighs 60g of carbon, you have ____ moles of carbons.
(1 mole of carbon is 12g). hint: 12g is 1 mole si 60 g is _______ moles ((proportions)
that is ____________ atoms of carbons.
(hint : use Avogadro number 1 mole = 12 g =6.02 1023 atoms so ........... proportion to solve)
If you weigh 100g of hydrogen gas (H2) you have __________ moles. hint: 1 mole of H2 = 2g
or _________ molecules of H2.
(hint: use Avogadro number 1 mole = 6.02 1023 molecules H2 so ... )
5)
A) 1 mole of H2 (hydrogen gas) = ________ g , 1 mole of N2 (nitrogen gas)= __________g, 1 mole of NH3 (ammonia) = __________ g (N + H + H + H)
B) Ammonia is an important chemical used for fertilizer. we know how to synthesize ammonia:
N2 + 3H2 = 2 NH3
1 mole of nitrogen gas reacts with __3____ moles of hydrogen gas to produce _________ moles of ammonia
So ______g of N2 reacts with _________ g of H2 to produce __________ g of NH3
( H2 in g ) (3 x N2 in g) (2 x NH3 in g )
(here is a cool website to practice balancing equations)
You get H2 from burning natural gas, N2 comes from the air. (20% oxygen and 80% nitrogen)
story:
The German chemist Fritz Haber is the one who discovered the making of ammonia in 1909. He gave Germany
an agriculture independence as the country didn't rely any more on South America to get Ammonia.
During world war I, by patriotism, he developed poisonous gas like chlorine. He is considered as the father
of chemical warfare. Haber was jewish and when the nazis came to power he was just
the jew Haber. He was exiled and died from heart attack in England. During the 1920s, scientists working at his institute developed
the cyanide gas formulation Zyklon B, which was used as an insecticide, especially as a fumigant in grain stores,
and also later, after he left the program, in the Nazi extermination camps, killing other Jews, including, with terrible irony, many of his relatives.
(source: wikipdia.org)
-----------------------------------------------------
7) The density of alcohol is 0.8g/ml. What is the weight of 50ml of alcohol ?
hint: 0.8g/ml means 0.8g for 1 ml. proportion again
8) The density of concentrated sulfuric acid is 1.85g/ml. What volume of the acid would weigh 74 g ?
hint: 1 ml = 1.85g so ...
9) One kilogram of metallic osmium, the heaviest substance known(atomic number is 76g), occupies a volume of 44.5 cm3. Calculate the density of osmium in grams
per cm3 (that is find the mass for 1 cm3 ). (hint; convert kg to g first, then set your proportion)
It is the densest natural element. Osmium is found in nature as an alloy, mostly in platinum ores
10) If the dot under a question mark (made with pencil) has a mass of 10-6g (micrograms), and you assume it is carbon, how many atoms are required to make
such a dot ?
hint: 1 mole of carbon is 12g and contains 6.02 1023 atoms so 10-6 g contains ..
11)
A) 1 mole of water H20 weighs _________ g ( H + H + O)
What is the approximate number of molecules in a drop of water which weighs 0.09g ?set your proportion
. 1 mole of water = _____ g (see A) and contains 6.02 1023 molecules H20 .so 0.09g contains ....... H20
12)
Consider the chemical reaction Mg + 2HCL = H2 + MgCL2
Magnesium (solid) reacts with Hydrogen chlorine (liquid) to produce hydrogen gas and magnesium chlorine.
A) mole of magnesium is _________g , 1 mole of HCL is __________g ( H + Cl), 1 mole of MgCl2 is _______g (Mg + Cl + Cl)
B) the formula shows that 1 mole of Mg reacts with _____ moles of HCL to produce _____ moles of hydrogen gas and ______ moles of MgCl2
so __________g of Mg reacts with __________g of HCL (2 moles of HCL) to produce _________g of H2 and ________ g of MgCl2
C)) 100g of Mg react with ______ g of HCL to produce _________ g of MgCl2
(proportion, use B)
13) (source) of the following problems:
A) 1.77 x 1028 atoms Cu = ___ mole Cu
= ___ grams Cu
B) 1.99 x 1025 molecules of H2O = ___ moles H2O
C) 0.667 moles Li = ___ g Li
D) 15.0 x 1023 atoms Zn = ___ g Zn
E) 4.75 x 106 atoms Al = ___ g Al
14)
A) what is 1 mole ?
B) define molar mass
C) state Avogadro number
15)
A) 0.250 mole Br = ___ atoms Br
B) 7.25 g Cu = ___ atoms Cu
16) fill the blanks
more problems (source)
16) REVIEW order of magnitude.
Consider the carbon atom. (average atom) with 12 nucleons inside.
If the atom (electronic cloud) is scaled up to a new year ball (about 1 m diameter)
a nucleon (proton or neutron) inside the nucleus would be the size of a human hair (about 20 micrometer diameter).
What is the order of magnitude ? (find the ratio between the ball's diameter and the hair diameter) _____ : 1 (in scientific notation)
That means the whole atom (nucleus + clouds of electrons) is ____________ times larger than the nucleon.
In a carbon you have ____ nucleons so the diameter of the nucleus is about ________ times smaller than the, whole atom.
17) if a nucleus is the size of a soccer ball (about 20cm across) the electronic cloud would be 9.5 miles away.
find the ratio between the size of the atom (9.5 miles) and the size of a nucleus (10cm).
Do you get about the same order of magnitude than before? (you need to convert miles to meter and cm to meter first)
18) REVIEW
10 trillion cells in our body = _____________ in scientific notation.
Each cell harbors 10 microbs. So ___________ (scientific notation) inhabit us.
If you take all our DNA strings, strtch them out and connect them you will
make 8000 round trips to the moon. How long is that in km (scientific notation) __________ km
(distance to the mooon, see problem 2)
PART2: ENVIRONMENT / ALTERNATIVE ENERGY
1) It is estimated that 2 105 tons of sulfur dioxide, SO2, enters the atmosphere daily owing to the burning of coal and petroleum products.
Assuming an even, distribution of the sulfur dioxide throughout the atmosphere , calculate in parts per million by weights the concentration
of SO2 added daily to the atmosphere. The weight of the atmosphere is 4.5 1015 tons.
hint: it is a proportion if: 2 105 is for 4.5 1015 then X is for 1 million
It takes about 40 days for the removal of acid sulfuric by rain. (acid rain that destroys trees and contaminates lakes )
2) source: Mathematics teaching in the middle school / Vol. 15 , No2, September 2009
Ethanol is now used as an alternative fuel. It is made from corns.
A) To measure the quantity of corns, farmer use a unit of mass called a bushel. 1 bushel is 56 pounds.
1 acre of corn field yields 150.7 bushels of corns. How many bushels can be produced on 300 acres ?
1000 acres ? Keep these numbers, you will need them for the coming questions.
(hint: set your proportion )
B) Only 15% of the corn produced is sent to an ethanol rafinery.
How many bushels are sent to rafinery from the corns grown on a 300 acres ?
1000 acres ?
(hint: proportion again 15 out of 100 is sent to rafinery . so use A) )
C) From each bushel, an thanol rafinery can produce 2.8 gallons of enthanol .
Using the numbers found in B) find the gallons of enthanol produced from the
corns grown from a 300 acres and from a 1000 acres
D) in 2008 9 billion gallons of ethanol was produced from rafineries.
Aprroximatly, how many bushels of corn were used in ethanol production?
(hint: use 1 bushel produces 2.8 gal )
PART 4: more problems ratio
1) REVIEW
0.0342 mm = ___________micrometers 0.00432 m = ________mm = _________ micrometers
4,232 micrometers = __________mm 2,000,000 micrometers = _________ m
4,232g = ________ kg 0.32 kg = ________g 3 tons = __________ kg
3,300 km = _________m 10-10 meters = _________ micrometers 10-2 meters = ________ mm
3.4 104 g = _________kg
2) REVIEW (in scientific notation)
1 billionth meter = _________ m 1 millionth meter = ____________m 1 thousandth gram= __________ g
20 million of million = _______________ 30 billion of billion = _____________ 1 hundredth = _________
1000 billion of molecules of proteins __________________.
3) a healthy person drinks 2 kg of water, eats 8kg of food and inhales 16 kg of air (only 20% of it is oxygen).
Whats is the ratio of weighs of air inhaled vs food eaten ?
4) The movie Austin Powers features Dr. Evil and his clone Mini Me. Mini Me is much smaller even if identical to Dr. Evil. Mini Me (in the movie) is said to me 1/8 of Dr Devil's size. Let's find out if this makes sense.
If Mini Me is 32 inches and 1/8 of Dr. Evil, how tall is Dr. Evil (in inches) ? Does this make sense ?
hint: the scale (ratio) is 1 inch (Mini ME) to 8 inches (Dr. evil). 1 foot = 12inches
5) In 2004, the population density (number of people per unit area) of the united states reached 80 people per square mile. How many people would you expect around Lake Wobegon, Minnesota, an area of 50 square miles?
hint: you are looking for people per square miles so divide people per square miles !
6) One of the MOST densely populated cities in Macao (a Chinese territory under Portuguese administration) with about 446,250 inhabitants living on 21 square kilometers of land. What is the population density per square kilometer in Macaw ? (that is the number of people per square kilometers) (hint: divide people by area)
hint: people per square kilometer. you divide.
7) According to Plato's description, the population of the lost city of Atlantis was between 6 and 10 millions people. If the area of Atlantis was 86,400 square kilometers and he population is assumed to have been 8,640,000 inhabitants, what was the population density for Atlantis (in people/km2) ?
8) Another densely population city is Monaco with 31,980 inhabitants living on 1.95 square kilometers of land. What is the population density per square kilometer in Monaco ?
9) A student is paid at the rate of $38 for 8 hours of work. What is the rate per hour?
hint: rate per hour means $ per hour so divide $ per hour !
10) Which is the fastest-growing plant you know ? A bamboo grew 36 inches in a 24 hour period. What was the hourly growth rate for this plant (in inches per hour that is in/hr)
That means: In every hour, the plant grows ____________, in 3 hours it grows ___________, in 1 day __________
hint: 1 day = 24 hours
11) The fruit with the lowest caloric value is the cucumber. A 11/2 pound cucumber as 109.5 calories. What is the caloric rate per pound of cucumbers ?
hint: that is calories per pound cal/lbs, remember: 11/2 = 1.5
12) A burger king hamburger has 275 calories and weighs 110 grams. Find the number of calories per gram.
13) THe fruit with the highest caloric value is the avocado: 1 1/2 pounds of edible avocado contain 1110 calories.
What is the caloric rate per edible pound ?
14) The air distance between New york and DAllas is 1375 miles. If a plane takes 21/2 hours to make the flight, what is the planet's rate of travel ? The rate represent the _____________ of the plane. (look at the units)
hint: Find the number miles traveled per hour . 2 1/2 = 2.50. Divide miles per hour. units = mph
15) One of the fastest marathon runners is Balaine Desimo, who completed 26 miles in 2.1 hours. TO the nearest mile, what was his rate of travel ?
hint: that is, find his speed = miles per hour =- miles/hours
16) elephants eat more than 1400 pounds of food a week How many pounds of food per day is that ?
hint: pounds per day. there are 7 days in a week
17) An AMerican alligator lives about 40 years and, during that time, grows about 3000 teeth, How many teeth per year is that ?
18) A Llama can travel 60 miles in three days. How many miles per day ?
19) you take a Microsoft Windows Professional class. It costs $698 for 21 hours. Find the cost per hour ?
20) A rhinoceros beetle weighs 30 grams and can carry 850 times its body weight, that is 25,500 grams. If a person could carry proportionally as much as the rhinoceros beetle, how much could a 60 kg student carry.(1 kg = 2.2 lbs)
hint: if you were are strong as that bug, you would be able to carry 850 times your mass (60kg). then convert to pounds.
21) A leaf-cutting ant weighting 1.5 grams can carry a leaf weighting 4.5 grams. If a person could proportionally carry as much weight, how much could a 60kg student carry?
hint: Find how many times (X) its body mass, the ant , can carry first. (4.5 / 1.5) = X. If the student is as strong , he would be able to carry also X times his mass.
Then convert kg to lbs.\
22) In the lab about ratios, you investigated the ratio between surface area versus volume. you found out that smaller objects have more? less ? area per unit mass than larger objects.
Scaling affects living organism. In the case of mammals, for example, size affects the life span of an organism. Small mammals live fast? slow ? and die young. Larger animals live at a leisurely pace and live __________.
23) Explain why if you were to scale up an moose to the size of an elephant, this animal would collapse.
(hint: the weight depends on the volume but the strength depends on the cross-sections of the limbs )
Fill the blank: As an animal gets larger it gets heavier but not ____________.
24) Find the product. Give the answer with the appropriate unit of measure.
I write fraction using slash. So one-third is 1/3, one half is 1/2, three-fifth is 4/5 ... you get it.
A) (3.5 hours) x 45 miles/1hour = ________ ______.
B) (500 dollars) x 12.2 schillings/1 dollar =
C) 3 dollars/1 square foot x (1222 square feet) =
D) (12 seconds) x 254feet /1 second = E)
E) (7meters/1minute) (60 minutes)
F) (168 hours/ 1 week) (52 weeks)
G) (3yards/1second) (12 seconds) - 10 yards
H) (15dollars / 1hour ) ( 8 hours) + 45 dollars
25) Monique uses 1.5 pounds of fertilizer for every 200 square feet of lawn. How many pounds of fertilizer will she have to use on a lawn that measured 3000 square feet?
26) In 10 years , the price of a scientific calculator went from $50 to $10. What is the ratio, as a fraction in simplest form, of the decrease in price to the original price?
27)
THe speed a boat travels is usually measured in nautical miles or knots. The Golden Gate-Sausalito ferry in California, which provides service between Sausalito and San Francisco, can travel at 20.5 knots. Find the speed in miles per hour. (1 knot = 1.15 miles per hour).
28) THe amounts of water typically used for common household tasks are given in the table below.
Find the number of liters needed for each task. (1 gallon = 3.79 liters)
| task | water used (gal) | water used (liter) |
| laundry (1 load) | 40 | |
| 5 minutes shower | 12.5 | |
| washing hands | 0.5 | |
| flushing toilet | 3.5 |
29) Lake Baikal, in Siberia, is so large that it would take all the rivers on Earth combined an entire year to fill it.
At 1.62 km deep, it is the deepest lake in the world. Find the depth of Lake Baikal in miles. (1mile = 1.6 km).