Chapter 5, Problem 5.37PAE

Interpretation Introduction

Interpretation:

The total pressure (in atm) of a 15.0-L container at 28°C that contains N₂, O₂ and Cl₂ has to be calculated.

Concept Introduction:

• An ideal gas has is a hypothetical gas that is formed by a few molecules so that, its density is low, and the intermolecular forces are null. The model of gas facilitates mathematical calculations to study gases.
• The ideal gas law can be expressed in the following way,

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

Where P is the gas pressure (atm), V is the gas volume (L), T is the gas absolute temperature (K), n is the moles number of the gas and R is the ideal gas constant ( $\text{R=0}\text{.082 }\frac{\text{atm L}}{\text{K mol}}$ )

$\text{Absolute temperature (K) = T (°C )+ 273}$. Where, T (°C) is the temperature in Celsius degrees (°C).

• The ideal gas mixture is a mixture of two or more ideal gases that has the following characteristics,
• Each component of the mixture behaves as ideal gas that occupies all the mixture volume at the mixture temperature.
• Each component exercises a partial pressure. The sum of the partial pressure of the components is equal to the total pressure of the mixture.
• The mole fraction is the ratio between the moles number of the component in the mixture and the total number of moles of gas in the mixture. It can be expressed in the following way,

${\text{y}}_{\text{i}}\text{=}\frac{{\text{n}}_{\text{i}}}{{\text{n}}_{\text{total}}}$

Where, y_i is the molar fraction of component i, n_i is the moles number of component i and n _total is the total moles number of the mixture.

• The partial pressure is the pressure that a gas of the mixture exercises if it occupies all the volume of the mixture.
• The partial pressure of each component in the mixture is directly proportional to its molar fraction. It can be expressed in the following way,

${\text{P}}_{\text{i}}={\text{y}}_{\text{i}}{\text{ x P}}_{\text{total}}$

Where, P_i is the partial pressure of component i, P_total is the total pressure of the mixture and y_i is the molar fraction of component i.