Question

Oxygen and cyclopropane at partial pressure of $570{\text{ }}torr$ and $170{\text{ }}torr$ 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?
\[
  A.{\text{ }}\dfrac{{170}}{{740}} = 0.23 \\
  B.{\text{ }}\dfrac{{170}}{{42}}/\left[ {\dfrac{{170}}{{42}} + \dfrac{{570}}{{32}}} \right] = 0.19 \\
  C.{\text{ }}\dfrac{{170 \times 42}}{{570 \times 32}} = 0.39 \\
  D.{\text{ }}\dfrac{{170}}{{570}} = 0.30 \\
 \]

Answer 1

Hint- In order to deal with this question first we will write the ideal gas equation for cyclopropane and oxygen then we will get the relation between the number of moles and pressure further by putting the values and taking the values of temperature and volume constant we will get the answer.

Complete step-by-step answer:
Formula used- $pV = nRT$
Given that
Partial pressure exerted by cyclopropane $ = 170{\text{ }}torr$.
Partial pressure exerted by oxygen $ = 570{\text{ }}torr$.
We know that ideal gas equation is given as
$pV = nRT$
Here p is the pressure, V is the volume of gas, n is the number of moles of gas, T is the temperature of the gas and R is the gas constant.
Let us consider cyclopropane as case (1)
${p_1}V = {n_1}RT$
Now consider case of oxygen as case (2)
${p_2}V = {n_2}RT$
Assuming volume and temperature constant in the above two equations and taking the ratio of case (1) and case (2) we get:
$
   \Rightarrow \dfrac{{{p_1}V}}{{{p_2}V}} = \dfrac{{{n_1}RT}}{{{n_2}RT}} \\
   \Rightarrow \dfrac{{{p_1}}}{{{p_2}}} = \dfrac{{{n_1}}}{{{n_2}}} \\
$
Thus, substituting the values of given pressure in the above equation we get:
$
  \because \dfrac{{{p_1}}}{{{p_2}}} = \dfrac{{{n_1}}}{{{n_2}}} \\
   \Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{170torr}}{{570torr}} \\
   \Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{170}}{{570}} = 0.3 \\
 $
Hence, the ratio of the number of moles of cyclopropane to the number of moles of oxygen is 0.3
So, the correct answer is option D.

Note- The ideal gas formula, also known as the general gas equation, is the equation of state of an ideal imaginary gas. This is a good approximation of other gases' behavior under several circumstances, but it has many drawbacks.