Law

Ideal Gas
Equation

Combined Gas
Law

equation 
P V
= n R T 
P_{1} V_{1} = P_{2} V_{2} T_{1} T_{2} 
explanation 
one gas at one set of conditions 
one gas that is changing conditions 
when to use it 
when the problem gives 3 of these: P, V, n, T 
more than one temperature, pressure, and/or
volume in the problem 
specific units req’d? 
pressure = atm volume = liters quantity (n) = moles temperature = Kelvins 
temperature = Kelvins pressure & volume can be any unit, but must
be the same unit on both sides of the equation 
Law

Boyle’s Law

Charles’ Law

GayLussac’s
Law

equation 
P_{1} V_{1} = P_{2} V_{2} 
V_{1} = V_{2} T_{1} T_{2} 
P_{1} = P_{2} T_{1} T_{2} 
explanation 
pressure & volume are inversely
proportional; temperature is constant 
volume & Kelvin temp of a gas are directly
proportional; P is constant 
pressure & Kelvin temp of a gas are directly
proportional; V is constant 
when to use it 
given 2 difft pressures & 1 volume or given
2 difft volumes & 1 pressure 
given 2 difft volumes & 1 temperature or
given 2 difft temperatures & 1 volume 
given 2 difft pressures & 1 temperature or
given 2 difft temperatures & 1 pressure 
specific units req’d? 
any  but must be the same on both sides of
equation 
any unit for volume (same on both sides), Kelvin
temperature 
any unit for pressure (same on both sides), Kelvin
temperature 
Law

Dalton’s Law

Dalton’s Law

Graham’s Law

equation 
P_{total}
= P_{gas1} + P_{gas2} +... 
P_{x}
= (moles gas X) . P_{total} (total moles) 
rate A = √MM B rate
B √MM A 
explanation 
the sum of the pressures of the individual gases
in a mixture equals the total pressure exerted by the mixture 
amount of a gas in mixture is proportionate to
the amount of its partial pressure 
rate of gas A compared to the rate of gas B is
equal to the square root of the inverse of their molar masses 
when to use it 
mixture of gases; only pressures given 
mixture of gases; moles & total pressure
given 
when any form of the word “effusion” or
“diffusion” is in the problem 
specific units req’d? 
any  but all values must have same unit of
pressure 
any  but all values must have same unit of
pressure 
no 
1.
Convert the following temperatures.
(A)
104 ^{o}C to K (B) 3 ^{o}C to K (C) 67 K to ^{o}C (D) 1671 K to ^{o}C
377 K 270
K 206 ^{o}C 1398
^{o}C
2.
Convert the following pressures.
(A)
635 torr to atm (B) 104.2 kPa
to mm Hg (C) 1.45 atm to Pa
0.836 atm 781.8 mm Hg 147,000 Pa
(146885 before rounding)
3.
A gas that effuses 1.19 times slower than nitrogen is added to light
bulbs. What is the
molecular mass of this unknown gas?
Rate N_{2} = √MM unknown 1.19 = √x x = 39.7 g/mole
rate
unknown √MM N_{2 } 1 √28
4.
(A) What is the molecular mass of a 0.2500 g sample of a gas at 99.8^{o}C
and 0.9131 atm
in a 100.0 cm^{3} container? (B) What is the gas in the container?
MM = gRT (0.2500 g) (0.0821 L^{.}atm/mole^{.}K)
(372.8 K) MM = 83.8 g/mole
PV (0.9131
atm) (0.1 L) Krypton
5.
A small 2.00 L fire extinguisher has an internal pressure of 506.6 kPa at 25^{o}C. What
volume of methyl bromide, the fire
extinguisher’s main ingredient, is needed to fill an
empty fire extinguisher at standard
pressure if the temperature remains constant?
P_{1}V_{1} = P_{2}V_{2} (506.6 kPa) (2.00 L) = (101.3
kPa) V_{2}
V_{2} = 10.0 L
6.
If 45.0 g of propane gas burns completely in the following reaction:
C_{3}H_{8(g) }+
5 O_{2(g) }→ 3 CO_{2(g)
}+ 4 H_{2}O_{(g)}
then how
many liters of carbon dioxide gas will be released if the system is at STP?
45.0 g
C_{3}H_{8}  1 mole = 1.023 moles C_{3}H_{8} 1.023 moles C_{3}H_{8}
= x moles CO_{2}
 44.0 g 1 3
X
= 3.069 moles CO_{2}  22.4 L = 68.7 L
 1 mole
7. Air in a closed cylinder is heated from 25°C to
36°C. If the initial pressure is 3.80 atm,
what is
the final pressure?
P_{1} = P_{2 } 3.80
atm = P_{2} P_{2} = 3.94 atm
T_{1} T_{2} 298 K 309 K
8. At what temperature Celsius will 19.4 g of
molecular oxygen, O_{2}, exert a pressure of
1820 mm
Hg in a 5.12 L cylinder?
PV = nRT 19.4
g O_{2}  1 mole = 0.60625
moles 1820 mm Hg  1 atm = 2.395 atm
 32 g  760 mm Hg
(2.395
atm) (5.12 L) = (0.60625 moles) (0.0821 L^{.}atm/mole^{.}K) T
T
= 246K > 27 ^{o}C
9.
To what temperature must 32.0 ft^{3} of a gas at 2.0 °C be heated for
it to occupy
1.00 x 10^{2} ft^{3} at
the same pressure? (ft^{3 }is a unit of volume)
V_{1} = V_{2} 32 ft^{3} = 100
ft^{3} T_{2} = 859 K or 586 ^{o}C
T_{1} T_{2 }275
K T_{2}
10.
Determine the molar mass of a gas that has a density of 2.18 g/L at 66°C and
720
mm Hg.
D = MM P 2.18
g/L = MM (0.947 atm) MM = 64 g/mole
RT (0.0821
L^{.}atm/mole^{.}K) (339 K)
11.
A 3.10 mL bubble of methane gas forms at the bottom of a bog where the temp
erature is 12^{o}C and the
pressure is 8.5 atm. The bubble rises to the surface where the
temperature is 35^{o}C and the
pressure is 1.18 atm. What is the new
volume of the
methane bubble?
P_{1}V_{1} = P_{2}V_{2} (8.5 atm) (3.10 mL) = (1.18
atm) V_{2}_{ } V_{2} = 24 mL
T_{1} T_{2} 285 K 295 K
12.
A mixture of 2.00 moles of H_{2}, 2.00 moles of NH_{3}, 4.00
moles of CO_{2} and 5.00 moles
of N_{2} exerts a total pressure
of 800. torr. What is the partial pressure of each gas?
P_{x}
= moles x .
P_{total} H_{2} and NH_{3} = 2.00 moles . 800 torr = 123 torr
total moles 13.00 moles
CO_{2} = 4.00 moles . 800 torr = 246 torr N_{2} = 5.00 moles . 800 torr
= 308 torr
13.00 moles 13.00
moles
13.
For the reaction 2 H_{2(g)} + O_{2(g)} → 2 H_{2}O_{(g)},
how many liters of water can be made from
5.0 L of oxygen gas and an excess of
hydrogen?
5.0 L O_{2} = x L H_{2}O x = 10. L
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