UNIT 10 NOTES- CHEM H- GAS LAWS II
The Ideal Gas Law
Ideal gases are gases whose particles take up no space(volume) and have no
intermolecular attractive forces.
The Ideal gas law is a combination of Boyle’s, Charles’, Gay-Lussac, and
Avagadro’s Law and used to describe the relationship amongst pressure, volume,
Temperature(K), and the number of moles of gas.
If the number of moles of gas is changed, then at least one of the other variables
will be affected. Mathematically the law states…
PV = n RT
Where :
P = pressure
V= Volume
n = moles
T = Temperature
R = Ideal Gas constant (depends on other units
Units of R
Numeric Units of P
Units of V
Units of T
al value
of R *
L-ATM /MOL K
0.0821
ATM
L
K
L-KPA / MOL K
8.314
KPA
L
K
L-MMHG /MOL K 62.4
MM HG
L
K
* Note that “Pressure unit” really determines the gas constant used.
Units of n
MOL
MOL
MOL
Sample Problem #1
Calculate the volume that a 88.0 g sample of CO2 gas will occupy at 265K and a pressure
of 0.900 Atm
First: convert “grams” into “moles” CO2
88.0 g CO2
1 mole CO2
44.0 g CO2
= 2.00 mole
Then: use the Ideal equation.
PV = nRT
0.900 ATM (V) = 2.00 mole (0.0821 atm/molK) 265K
V = 48.3 L
Notice that:
So…..
Mole = Grams
G. F. Wt.
PV = g
RT
M.Wt.
rearranging… P (GFW) = g = Density of gas(D) = M/V
RT
V
Sample Problem #2
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Calculate the volume of 1 mole of any gas at STP.
Gay-Lussac’s Law of Combining Volumes of Gases
Under the same conditions of temperature & pressure, the
volume of reacting gases and their gaseous products are
expressed in ratios of small whole numbers.

+
* 2 volumes H2 + 1 volume O2 
2 volumes H2O
Avogadro’s Principle
Equal volumes of all gases under the same conditions of
temperature and pressure contain the same number of
molecules. Therefore as the picture above shows:
2 volumes H2
+ 1 volume O2  2 volumes H2O
OR
2 molecules H2 + 1 molecule O2  2 molecules H2O
OR
12.04x1023 molecules H2 + 6.02x1023 molecule O2  12.04x1023 molecules H2O
* remember both are diatomic
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Molar Volume of a Gas
The volume occupied by 1 mole (or 6.02 x 1023 particles)
of any gas at STP.
Based on Avogadro the molar volumes of all gases must
be equal under the same conditions of temperature and
pressure.
This was determined experimentally to be equal to
22.4 L
aka
MOLAR VOLUME
1 mole H2 = 6.02 x 1023 molecules = 2.0 grams
1 mole CO2 = 6.02 x 1023 molecules = 44.0 grams
1 mole O2 = 6.02 x 1023 molecules = 32.0 grams
All gases, not just these!
Using Molar Volume to calculate Gas Density at STP (ONLY)
Earlier in the year we determined that:
Density = MASS (grams)
VOLUME (liters)
Since…. 1 mole weighs a mass equal to the GRAM FORMULA WEIGHT
1 mole of any gas occupies 22.4L at STP
Then we can find the density for 1 mole (or any amount) of gas at STP
Density = Gram F.Wt. = g/mole = g
22.4
L/mole
L
We can also equate the two density equations:
M = GRAM F. WT
V
22.4L
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Worksheet RR H Chem
Name________________
Ideal Gas Law PV=nRT …. and others
I. Complete the problems
II. What volume will 1.0 mole of any gas occupy at standard conditions?______
III. What are standard conditions ?
IV.
How can the density of a gas be calculated ?
What units are used for the mass? volume? Density of a gas , liquid,solid?
1. What volume does 0.20 mole H2 occupy at 0.821 atmospheres and a temperature of
30K ?
2. Some O2 , 750 ml is measured at a temperature of 25C
and 720 mm Hg pressure. How many moles of O2 is this ?
3. Find the volume of 10.00 g of CO2 gas at 20.0C and 740 mmHg pressure.
4. What is the mass of 2176 ml of SO2 collected at 39C and 750 torrs?
5. Find the volume of chlorine gas at 7C and 841 torr if it weighs 98 g.
6. At what Celsius temperature will 36g of water vapor be if the volume is 60.0 liters at a
pressure 902 torr ?
7. The weight of 325 ml of a gas collected at 9C and 750 mmHg is 0.68 gram . Find the
molecular weight.
8. The weight of 2.9 liters of a gas collected at 300C and 4.0 atmospheres is 5.98 gram.
Find the molecular weight.
**9. The weight of 445 ml of a gas at 30.0C and 675 mm Hg pressure is 8.11 gram.
Determine the density at STP.
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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10. A gas has a density of 1.429 g/L at STP. What is the Formula weight of the gas?
11. What is the mass of HCl if it occupies 12.8 L at STP ?
12. What is the volume of 125g of C5H12 at STP?
13. A 422ml sample of gas weighs 1.42 g. What is the gram formula weight (Molar
mass) of the gas ?
14. A gas has a density of 0.088 g/L. What is the molecular weight of the gas ?
15. What is the volume of 365 grams of ClO2 gas at STP ?
**16. A gas sample measuring 12,520 ml at 70 C and 911 torr weighs 12.3 g. What is the
density of the gas at STP?
17. Find the volume of Fluorine gas at 22 C and 890 torr if it weighs 103.0 g.
18. What is the weight of 29.4 liters of N205 at STP?
19. Determine the molecular weight of a gas if 850. ml of it weighs .95g at STP
20. The density of a gas at STP is 1.62 g/l. What is the density at 84 C and 109.7 kpa ?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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I. GRAHAM’S LAW OF DIFFUSION
The KMT describes gas molecules as being in constant motion. There are no
significant forces of attraction between molecules(Ideal Gas behavior). Thus gas
particles can flow easily past each other. This is attributed to the rapid motion of
molecules that arises from the vast amounts of free space between them.
Diffusion is defined as the spontaneous spreading of one type of gas molecule
through other gas molecules. Effusion is the rate in which a gas escapes through a small
opening.
As a result:
1. molecules with small masses move with higher speeds than those with large masses
and diffuse more rapidly.
2. Molecular weights and densities are inversely related to the rate of diffusion.
A Rate can be defined as a distance divided by a time.
Rate (speed) = distance
time
A Relative Rate is a comparison between 2 gases in the form of a ratio
Relative Rate = Rate gas1
Rate gas 2
Graham’s Law - The rates of diffusion(Effusion) of gases are inversely proportional
to the square roots of their molecular weights or densities. Mathematically, it states
Rate gas 1
M Wt. gas 2
=
Rate gas 2
M Wt. gas 1
OR
Rate gas 1
Rate gas 2
=
Density gas 2
Density gas 1
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Sample 1
Calculate the ratio of the rate of diffusion of Hydrogen gas to the rate of diffusion of oxygen gas.
Relative rate of Hydrogen gas to Oxygen gas = R H2
R O2
R H2
R O2
R H2
R O2
2
M Wt. H2
32.0 g/mol
=
R O2
R H2
M Wt. O
=
2.0 g/mol
=
4
1
Statement : Hydrogen gas diffuses 4 times more quickly than oxygen gas
OR....
R O2 =
R H2
1
4
Statement : Oxygen gas diffuses 1/4 times as fast as Hydrogen gas
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Worksheet SS Graham’s Law of Diffusion
I Which gases are the diatomic Gases?
II. What is the difference between “Rate” and “Relative rate” ?
II. PROBLEMS- Express all answers as a statement. Record three sig figs for all
answers.
1. Find the relative rates of diffusion of Helium gas and Argon gas.
2. Find the relative rates of diffusion of Radon gas and Argon gas.
3. How much faster is the diffusion rate of hydrogen gas compared to carbon dioxide ?
4. Compute the relative rate of diffusion for chlorine gas and ammonia.
5. The densities of helium and chlorine are 0.179 g/L and 3.17 g/L respectively. Calculate
the relative rate of diffusion.
6. If the density of Hydrogen is 0.090 g/L and the diffusion rate is 6 times that of
chlorine gas, what is the density of chlorine ?
7. What is the Molecular weight of a gas which diffuses 1/50 as fast as hydrogen ?
8. If the rate of flow of CH4 is 36.0ml/min, what is the rate of flow of C3H8 ?
9. If the rate of flow of H2S is 18.0ml/min, what is the rate of flow of Xe gas ?
10. Two porous containers are filled with hydrogen gas and neon respectively. Under
identical conditions, 2/3 of the hydrogen escapes in 6.0 hrs. How long will it take for half
the Neon to escape ?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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LAB - GRAHAM’S LAW OF DIFFUSION
Purpose- To find the relative rate of diffusion for Ammonia and Hydrogen chloride gas.
To compare the experimental relative rate to the Theoretical relative rate.
Diffusion is the spontaneous spreading out of molecules. The reasons for diffusion are as follows:
1. Molecules can diffuse because they are moving rapidly and have free space between each other.
2. Molecules of small mass move with higher speeds than large masses.
3. Therefore, diffusion rates of gases are inversely related to molecular weights or density.
Graham’s Law - The rates of diffusion of gases are inversely proportional to the square roots of their
molecular weights or densities. The Abbreviations/meanings are :
(R) Rate = Distance
M.W. = Molecular Weight
Relative rate w = Rate1
Time
Rate2
Mathematically; Graham’s law states that to find the Theoretical relative rate of 2 gases:
Rate1
Rate2
To find the Experimental relative rate:
in this lab
=
M.W. 2
M.W. 1
Rate NH3 = distanceNH3 / time
Rate Hcl
distance HCl / time
NH3 q-tip
HCl q-tip
PROCEDURE
1. Set up apparatus as shown above. Make sure glass tube is completely dry.
2. Break a Q-Tip and soak one end in HCl and the other in NH3.
3. Place Q-Tips into glass tube at same time. Keep aware of each Q-tips identity.
4. Watch for the formation of “RING” of smoke and mark first appearance with grease pencil.
5. Record distance form Ring to each Q-Tip. (cm)
6. Wash glass tube with distilled water.
7. Put used Q-Tips in beaker of water.
DATA
Distances of…
Ring to HCl end
Ring to NH3 end
TRIAL 1
TRIAL 2
cm
cm
cm
cm
1.Calculate the experimental Relative Rate for each trial:
2. Find the Theoretical relative rate using Molecular weights.
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Gas Stoichiometry
I. Volume-Volume Stoichiometry
Recall that Avogadro’s Principle stated that Equal volumes of all gases under the same
conditions of temperature and pressure contain the same number of molecules.
For the balanced equation ;
2H2 g + O2

g
2 H2O
g
+ 1 volume O2

2 volumes H2O
OR
2 molecules H2 + 1 molecule O2

2 molecules H2O
OR
12.04x1023 molecules H2 + 6.02x1023 molecule O2  12.04x1023 molecules H2O
OR
2.0 moles H2 +
1.0 mole O2
 2.0 moles H2O
2 volumes H2
In the balanced equation ;
2H2 g + O2

g
2 H2O
g
The coefficients can represent: molecules , moles, and VOLUME of a
GAS, because the same proportion exists for all .
In Volume- Volume Stoichiometry the volume of one gas is given and the
volume of a second gas is desired as the answer
SAMPLE PROBLEM #6
What Volume of Oxygen is needed to react with solid sulfur to form 3.5L SO3
The balanced equation is :
S8 (s)
+ 12 O2
(g)

8 SO3
(g)
Since both substances are gases, the relation from the balanced equation:
12 L O2 = 8 L SO3 can be used.
3.5 L SO3
12 L O2 = 5.25 L O2
8 L SO3
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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II. Mass-Volume Stoichiometry
In Mass- Volume Stoichiometry the Mass of one substance is given and the
volume of a second gas is desired as the answer, or vice versa. If the
conditions of temp and Pressure are not stated, you can assume Standard
conditions.
SAMPLE PROBLEM #7
What Mass of Calcium Carbonate is needed to decompose in order to form 4.00L of
carbon dioxide gas ?
The balanced equation is :
1 CaCO3 (s)

1 CaO
+
1 CO2 (g)
Since CO2 is a gas, liters can be converted to moles using 22.4 L = 1 mol @STP
4.00 L CO2
1 mole CO2
22.4 L CO2
1 mol CaCO3
1 mol CO2
100.1 g CaCO3 __ = 17.9 g CaCO3
1 mol CaCO3
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Worksheet TT
Name__________________
H Chem easy Gas stoichiometry: vol-vol & mass-vol
I. Complete the problems below in your notebook or separate paper.
1. What volume of hydrogen gas is needed to combine with 80 liters of Nitrogen gas to
form ammonia gas , at STP. : N2
+
H2

NH3
b) How many grams of hydrogen is required to combine with 8.0 liters of nitrogen to
form ammonia gas at STP ?
2. How many liters of oxygen are required to burn 20 liters of propane, C3H8 ?
C3H8
+
O2

H2O +
CO2
3. How many liters of CO2 will be produced by burning with 12.0L of oxygen in the
reaction,
C2H6 +
O2

H2O +
CO2
4. How many liters of chlorine gas are required to react with 24 liters of CH4 to obtain
CH3Cl and H2 ?
5. How many grams of S8 would have to be burned to produce 2.24 L of SO2 at STP?
S8 + 8 O2  8SO2
6. If 4.48 liters of ammonia gas are used, how many liters of oxygen are needed to react?
4NH3 + 5 O2  4NO + 6H2O
7. C4H10 reacts with oxygen to produce carbon dioxide & water vapor. How many liters
of oxygen is needed to produce 2.0 L of carbon dioxide?
8. Using the same equation as in question 7, if 15 L of O2 are used, how many liters of
C4H10 will be burned?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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9. Given the equation:
C10H22 +
O2 
CO2 +
H2 O
If a stove burns 1000g C10H22 how many liters of oxygen are needed? How many liters of
CO2 are produced?
10. In the following reaction how many liters of oxygen are used when 100 L of H2S are
burned:
H2S + O2 
SO2 +
H2O (be sure to balance)
11. Zinc reacts with hydrochloric acid. How many grams of zinc would be needed to
produce enough hydrogen to fill an 11.2 L balloon?
12. Silicon dioxide + carbon  carbon monoxide + silicon. If 140g of Si are produced,
what volume of carbon monoxide is also produced?
13. Given the formula: 2ZnS + 3 O2 2ZnO + 2SO2
How many liters of oxygen are needed to produce 300. g of ZnO and how many liters of
SO2 are produced if 100. g of ZnS are used?
14. How many grams of sodium are needed to release 4.0 liters of hydrogen gas from
water at STP ?
Na
+
HOH 
NaOH
+
H2
15. How many grams of copper II Oxide are needed to react with 28.0 liters of
Hydrogen?
CuO +
H2

Cu
+
HOH
16. How many liters of hydrogen gas form when 24.05g of Al react with sulfuric acid ?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Worksheet UU H chem
NAME _________________
More Involved Gas Laws - things you know from the past (we hope)
I. Complete the problems.
1. A gas sample, mass 0.467 g is collected by water displacement at 20. C and 750. torr.
Its volume is 200. ml. What is the molecular weight of the gas?
2. What volume of oxygen collected by water displacement at 20. C and 750.0 mm Hg
can be obtained by the decomposition of 55.0 g of potassium chlorate?
3. When 125 g of zinc reacts with 125 g of hydrochloric acid, how many liters of
hydrogen are formed?
4. If 40.0 ml of hydrogen measured at 22 C and 738 mm pressure is to be prepared from
magnesium and HCl, how many grams of magnesium must be used?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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5. What is the molecular weight of a gas if 11.6 g of the gas occupies 10.4 L at
750. mm Hg and 29.0 C
6. A gaseous compound has the analysis: nitrogen 63.64%, oxygen 36.36%, and a density
of 1.977 g/L. Determine a) the empirical formula b) the molecular formula and c) the
molecular weight
7. A deep underground cavern contains 2.24 x 10 6L of methane at a pressure of 15.0 atm
and a temperature of 42 C. How many grams of methane (CH4) are there?
8. How many grams of sodium chloride could be produced from the reaction of 23.0 g of
sodium with 22.4 dm3 of chlorine?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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9. Determine how many dm3 of CO2 at 27 C and 104.5 kPa can be produced from 15.7 g
of Fe2O3 and 11,200 cm3 of CO if Fe2O3 + 3CO ---> 2Fe + 3CO2
10. What is the molecular mass of a gas if 150.0 cm3 has a mass of 0.922 g at 99 C and
107.0 kPa?
11. A reaction between 5.0 g Aluminum and 34 g of H2SO4 will form how many liters
of hydrogen gas ?
12. 400.0ml of hydrogen measured at 20C and 740mm Hg is to be prepared by reacting
magnesium with HCl. What mass of magnesium is required ?
13. How many liters of hydrogen gas , collected by water displacement at 25C and
755mm Hg pressure, can be obtained from 6.0 g of magnesium and an excess of sulfuric
acid?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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Optional - Gas Law Review
Rah! Rah! Rah! (These are really simple)
1. Carbon monoxide & oxygen combine to form carbon dioxide. If 5.0 L of oxygen are
used, how many liters of carbon dioxide are produced?
2. Compute the relative rate of diffusion of oxygen & krypton.
3. Compute the volume of 11.0 g of N2O at STP?
4. What is the weight of one liter of ammonia?
5. Given the equation: ____Al2O3 ----> _____ Al + _____ O2, how many liters of
oxygen would be made using 408 g of aluminum oxide?
6. How many moles of gas will a 486 ml flask hold at 10 C and 500. mm Hg?
7. Calculate the relative rate of diffusion of hydrogen and bromine.
8. How many liters of hydrogen are needed to react with 4.0 L of nitrogen to form NH3?
9. A volume of 475 ml at 35 C & 815 torr has a weight of 0.768 g. What is the molecular
weight?
10. How many grams of calcium carbonate must be decomposed to produce 4.0 L of CO2
at STP?
11. If NH3 flows at a rate of 40. mm/min, what is the rate of flow for helium?
12. What pressure is exerted by .250 mol of CO2 at 100 C if it occupies 0.275 L?
13. How many grams of chlorine are contained in a 10.0 L flask at 100 C and 900. torr?
Mr Treuer Chem H Notes 2011-12 Unit 10 Gas Laws II
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