14.4. Gas Mixtures and Molecular Speeds http://www.ck12.org
Step 1: List the known quantities and plan the problem.
Known
- molar mass of NH 3 = 17.04 g/mol
- molar mass of HCl = 36.46 g/mol
Unknown
- velocity ratio vNH 3 /v
HCl
Substitute the molar masses of the gases into Graham’s law and solve for the ratio.
Step 2: Solve.
vNH 3
vHCl=
√
36. 46 g/mol
17. 04 g/mol= 1. 46
The rate of diffusion of ammonia is 1.46 times faster than the rate of diffusion of hydrogen chloride.
Step 3: Think about your result.
Since ammonia has a smaller molar mass than hydrogen chloride, the velocity of its molecules is greater, and the
velocity ratio is larger than 1.
Practice Problem- Determine the ratio of effusion rates for hydrogen gas and argon gas at the same temperature and pressure.
- A certain gas is observed to diffuse 3.32 times slower than helium. Calculate the molar mass of the gas.
The relative rates of diffusion for ammonia and hydrogen chloride from Sample Problem 14.10 can be observed in
a simple experiment. Cotton balls are soaked with solutions of ammonia and hydrogen chloride (hydrochloric acid)
and attached to two different rubber stoppers. These are simultaneously plugged into either end of a long glass tube.
The vapors of each travel down the tube at different rates. Where the vapors meet, they react to form ammonium
chloride (NH 4 Cl), a white solid that appears in the glass tube as a ring (Figure14.16).
FIGURE 14.16
Graham’s law can be demonstrated by a
glass tube capped on either end with cot-
ton balls that have been soaked in ammo-
nia or hydrochloric acid. The NH 3 vapor
travels faster down the tube than the HCl
vapor, as evidenced by the location of the
ring of ammonium chloride.The ring of ammonium chloride appears closer to the HCl end of the tube, indicating that the ammonia vapor has
diffused faster than the hydrogen chloride vapor.