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  • A vessel contains a mixture consisting of of nitr

A vessel contains a mixture consisting of \mathrm{m}_{1}=7 \mathrm{~g} of nitrogen \left(\mathrm{M}_{1}=28\right)$ and $\mathrm{m}_{2}=11 \mathrm{~g} of carbon dioxide \left(M_{2}=44\right)  at temperature T=300 \mathrm{~K} and pressure \mathrm{p}_{0}=1 \mathrm{~atm}. Find the density of the mixture.

Option: 1

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Option: 2

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Option: 3

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Option: 4

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Answers (1)

best_answer

Let  \mathrm{V} be the volume of the vessel. Then \rho_{\text {mis }}=\frac{\mathrm{m}_{1}+\mathrm{m}_{2}}{\mathrm{~V}}

Let \mathrm{p}_{1} and \mathrm{p}_{2} be the partial pressure

Then \mathrm{p}_{1} \mathrm{~V}=\frac{\mathrm{m}_{1}}{\mathrm{M}_{1}} \mathrm{RT}$ and $\mathrm{p}_{2} \mathrm{~V}=\frac{\mathrm{m}_{2}}{\mathrm{M}_{2}} \mathrm{RT}, \mathrm{p}_{0}=\mathrm{p}_{1}+\mathrm{p}_{2}

\therefore \quad \mathrm{p}_{0}=\left(\frac{\mathrm{m}_{1}}{\mathrm{M}_{1}}+\frac{\mathrm{m}_{2}}{\mathrm{M}_{2}}\right) \frac{\mathrm{RT}}{\mathrm{V}}
\mathrm{\therefore \quad \rho_{\text {mix }}=\frac{\left(m_{1}+m_{2}\right) M_{1} M_{2}}{m_{1} M_{2}+m_{2} M_{1}} \times \frac{p_{0}}{R T}}
\mathrm{=\frac{(7+11) \times 28 \times 44 \times 10^{-3}}{7 \times 44+11 \times 28} \times \frac{10^{5}}{8.3 \times 300}}

\mathrm{=1.446 \mathrm{~kg} \mathrm{~m}^{-3}=1.446 \: per\: litre}

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