Chapter 14, Problem 89A

Interpretation Introduction

Interpretation: The gas that diffuses at a faster rate from hydrogen chloride and ammonia should be interpreted when two ends of a tube are closed by cotton balls soaked with hydrogen chloride and ammonia to form the white solid ammonium chloride.

Concept Introduction: Graham’s law of effusion states that the rate of diffusion of any gas is always inversely proportional to the square root of the mass of gaseous particles. The mathematical expression for this law is:

  $\frac{\text{Rate of diffusion of gas 1}}{\text{Rate of diffusion of gas 2}}\text{=}\sqrt{\frac{\text{M2}}{\text{M1}}}$

Answer to Problem 89A

Ammonia will diffuse faster due to its lower molecular mass.

Explanation of Solution

Gases can diffuse and effuse due to the high kinetic energy of the gaseous particles. The rate of effusion of gases is directly proportional to their temperature of it and also depends on the molar mass of the gases.

  $\frac{\text{Rate of diffusion of gas 1}}{\text{Rate of diffusion of gas 2}}\text{=}\sqrt{\frac{\text{M2}}{\text{M1}}}$

Molar mass of hydrogen chloride = $\text{36}\text{.5 u}$

Molar mass of ammonia = $\text{17}\text{.0 u}$

Since the rate of diffusion of a gas is inversely proportional to the molar mass of the gas molecules. Since the molar mass of ammonia is lesser than that of hydrogen chloride so ammonia will diffuse faster than hydrogen chloride and solid ammonia chloride will form close to the cotton ball of hydrogen chloride.

Conclusion

As the molar mass of gas molecules increases, the rate of diffusion will decrease.