Transcript V. Two More Gas Laws
Ch. 10 & 11 - Gases
V. Two More Laws (p. 365-367, 386-388) Read these pages first!
B. Dalton’s Law
The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.
P total
= P
1
+ P
2
+ ...
When a H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor.
B. Dalton’s Law
Hydrogen gas is collected over water at 22.5
°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.
The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.
GIVEN: P H2 = ?
P P total H2O = 94.4 kPa = 2.72 kPa Look up water-vapor pressure on p.899 for 22.5
° C.
WORK: P total = P H2 + P H2O 94.4 kPa = P H2 + 2.72 kPa P H2 = 91.7 kPa Sig Figs: Round to least number of decimal places.
B. Dalton’s Law
A gas is collected over water at a temp of 35.0
°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.
GIVEN: P gas = ?
P P total H2O = 742.0 torr = 42.2 torr Look up water-vapor pressure on p.899 for 35.0
° C.
WORK: P total = P gas + P H2O 742.0 torr = P H2 + 42.2 torr P gas = 699.8 torr Sig Figs: Round to least number of decimal places.
C. Graham’s Law
Diffusion
• Spreading of gas molecules throughout a container until evenly distributed.
Effusion
• Passing of gas molecules through a tiny opening in a container
C. Graham’s Law
Speed of diffusion/effusion
• Kinetic energy is determined by the temperature of the gas.
• At the same temp & KE, heavier molecules move more slowly.
Larger
m
smaller
v
KE = ½mv
2
C. Graham’s Law
Graham’s Law
• Rate of diffusion of a gas is inversely related to the square root of its molar mass.
• The equation shows the ratio of Gas A’s speed to Gas B’s speed.
v A v B
m B m A
C. Graham’s Law
Determine the relative rate of diffusion for krypton and bromine.
The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “v A /v B ”.
v A v B
m B m A v Kr v Br 2
m m Br 2 Kr
159.80 83.80 g/mol g/mol
1.381
Kr diffuses 1.381 times faster than Br 2 .
C. Graham’s Law
A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions?
v A v B
m B m A v H 2 v O 2
m O 2 m H 2 v H
2
12.3
m/s
32.00 g/mol 2.02
g/mol
Put the gas with the unknown speed as “Gas A”.
v H
2
12.3
m/s
3.980
v H
2
49.0 m/s
C. Graham’s Law
v v A B v A v O 2
An unknown gas diffuses 4.0 times faster than O 2 . Find its molar mass.
The first gas is “Gas A” and the second gas is “Gas B”. The ratio “v A /v B ” is 4.0.
m m m m B A O A 2
Square both sides to get rid of the square root sign.
16
32.00 g/mol m A m A
32.00 g/mol 16
2.0 g/mol
2
TEAM PRACTICE!
Work the following problems in your book. Check your work using the answers provided in the margin.
• p. 324 SAMPLE PROBLEM 10-6 PRACTICE 1 & 2 • p. 355 SAMPLE PROBLEM 11-10 PRACTICE 1, 2, & 3