Question

A vessel contains a mixture of nitrogen ($m_1=$ 7.0 g) and carbon dioxide ($m_2=$ 11 g) at a temperature T $=$ 290 K and pressure $p_0=$ 1.0 atm. Find the density of this mixture, assuming the gases to be ideal.

• A. $1.5kg/m^3$
• B. $4.5kg/m^3$
• C. $3.5kg/m^3$
• D. $2.5kg/m^3$

Answer 1

The correct option is A $1.5kg/m^3$

Let the volume occupied by the mixture be $V$.

By Dalton's law of partial pressures, pressure of nitrogen is given by $\frac{P_{\text{nit}}}{P_0}=\frac{n_{\text{nit}}}{n_{\text{nit}}+n_{\text{car}}}$

Number of moles of nitrogen $n_{\text{nit}}=\frac{m_1}{M_{\text{nit}}}=\frac{7}{28}=0.25\text{mol}$

Number of moles of carbon $n_{\text{car}}=\frac{m_2}{M_{\text{car}}}=\frac{11}{44}=0.25\text{mol}$

Thus, $P_{\text{nit}}=P_0\times \frac{0.25}{0.25+0.25}=P_0/2=0.5\text{atm}$

From Ideal gas equation, $V=\frac{nRT}{P}=\frac{0.25\times 8.314\times 290}{0.5\times 101325}\approx 0.0119{\text{m}}^3$

Total mass of the mixture $m=7+11\text{g}=(7+11)\times {10}^{-11}\text{kg}$

Thus, density is $\rho =\frac{m}{V}=\frac{(7+11)\times {10}^{-3}}{0.0119}\approx 1.51{\text{kg/m}}^3$