Q49PE - College Physics (Urone)

Question

Question: Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when the atmospheric pressure is 1.01×10⁵ N/m²?

Step-by-Step Solution

Answer

Answer

The partial pressure of nitrogen is  $7.89\times {10}^{4}N/m^2$

Step 1: Introduction

We apply the formula for partial pressure which is to find partial pressure by multiplying nitrogen percentage by total pressure.

Step 2: Given parameters and formula for partial pressure

Total pressure = Atmospheric pressure =$\text{1.01}\times {\text{10}}^{\text{5}}{\text{N/m}}^2$

Percentage of nitrogen =78.1%

The formula for partial pressure ${\text{P}}_{\text{partial}}\text{ = }\frac{\text{\% Nitrogen}}{\text{100}}\times {\text{P}}_{\text{total}}$

Here, P_partial partial pressure and P_total   total pressure.

Step 3: Calculate the partial pressure

The partial pressure of nitrogen in the atmosphere

$$\begin{gathered} {\text{P}}_{\text{partial}}=\frac{\%Nitrogen}{100}\times {\text{P}}_{\text{total}} \\ {\text{P}}_{\text{partial}}=\frac{{\displaystyle 78.1(1.01\times {10}^5{\text{N/m}}^2)}}{{\displaystyle 100}}\times {\text{P}}_{\text{total}} \\ {\text{ =7.89×10}}^4{\text{N/m}}^2 \end{gathered}$$

Therefore, partial pressure of nitrogen is  \({\rm{7}}{\rm{.89 \times 1}}{{\rm{0}}^{\rm{4}}}\;{\rm{N/}}{{\rm{m}}^{\rm{2}}}\)