Question

(a) Calculate the mass of nitrogen present in a volume of 3000 cm³if the gas is at 22.0°C and the absolute pressure of 2.00${\mathbf{10}}^{\mathbf{-}\mathbf{13}}$atm is a partial vacuum easily obtained in laboratories. (b) What is the density (in kg/${\mathit{m}}^{\mathbf{3}}$) of the${\mathit{N}}_{\mathbf{2}}$?

Short answer

1. Mass of nitrogen is$6.95\times {10}^{-16}kg$
2. Density of $N_2$is $2.32\times {10}^{-13}kg/m^3$

Step-by-step solution

Ideal Gas Equation

Given data:

_{$$\begin{gathered} V=3000\times {10}^{-6}{m}^3 \\ T=295K \\ P=2\times {10}^{-13}atm \end{gathered}$$}

Calculating (n) by using the Ideal gas equation

_{$$\begin{gathered} PV=nRT \\ n=\frac{PV}{RT} \\ n=\frac{2\times {10}^{-13}\times 1.013\times {10}^5\times 3\times {10}^{-3}}{8.315\times 295} \\ n=2.48\times {10}^{-14} \end{gathered}$$}

Mass of Nitrogen

The mass of$N_2$is $m=n\times M$

Here$M=28\times {10}^{-3}kg/mol$

So, the mass is

_{$$\begin{gathered} m=n\times M \\ =2.48\times {10}^{-14}\times 28\times {10}^{-3} \\ =6.95\times {10}^{-16}kg \end{gathered}$$}

Mass of nitrogen is$6.95\times {10}^{-16}kg$.

Density of nitrogen

For density of$N_2$

_{$$\begin{gathered} \rho =\frac{m}{V} \\ =\frac{6.95\times {10}^{-16}}{3\times {10}^{-3}} \\ =2.32\times {10}^{-13}kg/m^3 \end{gathered}$$}

Therefore, Density of_{$N_2$} is$2.32\times {10}^{-13}kg/m^3$.