Chapter 14, Problem 85A

Interpretation Introduction

Interpretation: The number of particles of two gases should be compared if their partial pressure in a container were identical.

Concept introduction:

Under Standard pressure and temperature conditions, gases behave like Ideal gases. The variables of the ideal gas law can be determined with the help of the ideal gas equation. The mathematical relation of these variables can be calculated with the help of the given gas law.

  $\text{P}\times \text{V = n}\times \text{R}\times \text{T}$

The ideal gas law is the combination of all the gas laws like Boyle’s law, Charles’s law, etc.

Answer to Problem 85A

If the partial pressure of two gases is the same in a container of constant volume, the number of molecules must be the same.

Explanation of Solution

Boyle’s law states that at constant temperature and number of moles the pressure of gas must be inversely promotional to the volume. Similarly, Charles’s law states that the volume of gas is directly proportional to the temperature at constant pressure and the number of molecules.

If the partial pressure of two gases is the same in a container of constant volume, the number of molecules must be the same.

This is because as the number of particles increases in a gas, the frequency of collisions with the walls must increase increasing the gaseous pressure. In other words, the pressure of a gas is directly related to the number of particles in the gas.

Conclusion

The frequency of collisions between the wall of the container and gas particles causes gaseous pressure.