Question

A vessel is filled with a mixture of oxygen and nitrogen. At what ratio of partial pressure will the mass of the gases be identical?

• A. $p\left(O_2\right)=0.785p\left(N_2\right)$
• B. $p\left(O_2\right)=8.75p\left(N_2\right)$
• C. $p\left(O_2\right)=11.4p\left(N_2\right)$
• D. $p\left(O_2\right)=0.875p\left(N_2\right)$

Answer 1

The correct option is D $p\left(O_2\right)=0.875p\left(N_2\right)$

As $P\propto \chi \therefore \frac{P_{\left(O_2\right)}}{P_{\left(N_2\right)}}=\frac{{\chi }_{\left(O_2\right)}}{{\chi }_{\left(N_2\right)}}=\frac{n_{\left(O_2\right)}}{n_{\left(N_2\right)}}=\frac{w_{\left(O_2\right)}/M_{\left(O_2\right)}}{w_{\left(N_2\right)}/M_{\left(N_2\right)}}$
but given that $w_{\left(O_2\right)}=w_{\left(N_2\right)}$
$\Rightarrow \frac{P_{\left(O_2\right)}}{P_{\left(N_2\right)}}=\frac{M_{\left(N_2\right)}}{M_{\left(O_2\right)}}=\frac{28}{32}=0.875$