Question
Cyclopropane and oxygen at partial pressures $$170\,torr$$ and $$570\,torr$$ are mixed in a gas cylinder. What is the ratio of the number of moles of cyclopropane to the number of moles of oxygen?
A.
$$\frac{{170 \times 42}}{{570 \times 32}} = 0.39$$
B.
$$\frac{{170}}{{42}}/\left( {\frac{{170}}{{42}} + \frac{{570}}{{32}}} \right) \approx 0.19$$
C.
$$\frac{{170}}{{740}} = 0.23$$
D.
$$\frac{{170}}{{570}} = 0.30$$
Answer :
$$\frac{{170}}{{570}} = 0.30$$
Solution :
$$\eqalign{
& {\text{According to ideal gas equation,}} \cr
& {p_1}V = {n_1}RT\,\,\,...({\text{i}}) \cr
& {p_2}V = {n_2}RT\,\,...({\text{ii}}) \cr
& {\text{From Eqs}}{\text{. (i) and (ii)}} \cr
& \frac{{{p_1}V}}{{{p_2}V}} = \frac{{{n_1}RT}}{{{n_2}RT}} \Rightarrow \frac{{{p_1}}}{{{p_2}}} = \frac{{{n_1}}}{{{n_2}}} \cr
& \frac{{{n_1}}}{{{n_2}}} = \frac{{{p_1}}}{{{p_2}}} = \frac{{170}}{{570}} = 0.30 \cr} $$