Chapter 14.4, Problem 43LC

Interpretation Introduction

Interpretation: To determine the pressure of nitrogen.

Concept Introduction: According to Dalton's law, a combination of non-reacting gases exerts a total pressure equal to the average of the partial pressures of the constituent gases.

Answer to Problem 43LC

The pressure of nitrogen will be 191.3 $\text{kPa}$

Explanation of Solution

The given data:

The total pressure of the tire = $\text{245}\text{kPa}$

The partial pressure of ${\text{PO}}_{\text{2}}$ = $\text{51}\text{.3 kPa}$

The partial pressure of ${\text{PCO}}_2$ = $\text{0}\text{.10 kPa}$

The partial pressure of others = $\text{2}{\text{.3 kp}}_{\text{a}}$

The partial pressure of ${\text{pN}}_{\text{2}}$ =?

By using the Dalton law:

  $\text{P}\left(\text{total}\right)\text{ = p}₁\text{+ p}₂\text{+ p}₃\text{+ }\mathrm{............}{\text{+p}}_{\text{n}}$

Now, put the given data in the above equation.

  $\begin{array}{l}\text{p}\left(\text{total}\right){\text{ = pO}}_2{\text{+ pCO}}_2\text{+ p}\left(\text{others}\right){\text{+ pN}}_2\hfill \\ \text{245 kPa = 51}\text{.3 kPa + 0}\text{.10 kPa + 2}{\text{.3 kPa + pN}}_2\hfill \\ {\text{245 kp}}_a\text{ = 53}{\text{.7 kPa+ PN}}_2\hfill \\ \begin{array}{c}{\text{pN}}_2\text{= 245 kPa}-\text{53}\text{.7 kPa}\\ \text{=}191.3\text{ kPa} \end{array}\hfill \\ \hfill \end{array}$

The pressure of nitrogen = $191.3\text{ kPa}$