Chapter 5.3, Problem 5.5AFP

Interpretation Introduction

Interpretation:

The final pressure of nitrogen gas that occupies volume of $\text{2}\text{.55}\text{L}$ at $755\text{mmHg}$ and $23°\text{C}$ and changes to volume $\text{4}\text{.10}\text{L}$ at $18°\text{C}$ is to be calculated.

Concept introduction:

Ideal gas law equation is as follows:

$PV=nRT$ (1)

Here,

$P$ is the pressure of the gas.

$V$ is the volume occupied by gas.

$n$ is the number of moles of gas.

$T$ is the temperature in Kelvin.

$R$ is the universal gas constant.

For two different values of pressure, temperature, volume and number of moles equation (3) can be modified as follows:

$\frac{P_1{V}_1}{n_1{T}_1}=\frac{P_2{V}_2}{n_2{T}_2}$ (2)

Here,

$P_1$ is the initial pressure of the gas.

$P_2$ is the final pressure of the gas.

$V_1$ is the initial volume of gas.

$V_2$ is the final volume of gas.

$n_1$ is the initial number of moles of gas.

$n_2$ is the final number of moles of gas.

For fixed number of moles equation (2) can be written as follows:

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$ (3)

The conversion factor to convert $°\text{C}$ to Kelvin is as follows:

$T\left(\text{K}\right)=T\left(°\text{C}\right)+273.15$ (4)