Question
Cyclopropane and oxygen at partial pressures 170 $$torr$$ and 570 $$torr$$ respectively are mixed in a gas cylinder. What is the ratio of the number of moles of cyclopropane to the number of moles of oxygen $$\left( {\frac{{n{C_3}{H_6}}}{{n{O_2}}}} \right)?$$
A.
$$\frac{{170 \times 42}}{{570 \times 32}} = 0.39$$
B.
$$\frac{{\frac{{170}}{{42}}}}{{\left( {\frac{{170}}{{42}} + \frac{{570}}{{32}}} \right)}} \approx 0.19$$
C.
$$\frac{{170}}{{740}} = 0.23$$
D.
$$\frac{{170}}{{570}} = 0.30$$
Answer :
$$\frac{{170}}{{570}} = 0.30$$
Solution :
$$\eqalign{
& {\text{By ideal gas equation,}} \cr
& {P_1}V = {n_1}RT \cr
& {n_1} \propto {P_1}\,{\text{and}}\,{n_2} \propto {P_2} \cr
& \frac{{{n_1}}}{{{n_2}}} = \frac{{{P_1}}}{{{P_2}}} \Rightarrow \frac{{{n_1}}}{{{n_2}}} = \frac{{170}}{{570}} = 0.30 \cr} $$