Question

A vessel at 987 torr contains nitrogen, argon, helium and carbon dioxide gases. The partial pressure of the first three gases are $44.0{\text{mmHg}}$, $466{\text{mmHg}}$, and $220{\text{mmHg}}$ respectively. What is the partial pressure of carbon dioxide in atm?
A.$1.30{\text{atm}}$
B.$2.00{\text{atm}}$
C.$0.338{\text{atm}}$
D.$0.961{\text{atm}}$

Answer 1

To answer this question, you must recall Dalton's law of partial pressures. It states that the total pressure of a mixture of a number of non-reacting gases is equal to the sum of pressures exerted by the individual gases.
Formula Used: ${{\text{P}}_{\text{T}}} = {{\text{p}}_{\text{1}}} + {{\text{p}}_{\text{2}}} + ........{{\text{p}}_{\text{n}}}$
Where, ${{\text{P}}_{\text{T}}}$ is the total pressure of the mixture of gases
${{\text{p}}_{\text{1}}}{\text{,}}{{\text{p}}_{\text{2}}}{\text{,}}....{{\text{p}}_{\text{n}}}$ are the partial pressures exerted by the individual gases in the mixture.

Complete step by step answer:
We are given the total pressure of the mixture, so, we can write, ${{\text{P}}_{\text{T}}} = 987{\text{torr}}$
Also, we have the partial pressures exerted by nitrogen, argon and helium. We can write them as,
${{\text{p}}_{{{\text{N}}_{\text{2}}}}} = 44.0{\text{mmHg}}$
${{\text{p}}_{{\text{Ar}}}} = 466{\text{mmHg}}$
${{\text{p}}_{{\text{He}}}} = 220{\text{mmHg}}$.
We have to find the partial pressure of carbon dioxide in the mixture.
We can assume the partial pressure of carbon dioxide as:
${{\text{p}}_{{\text{C}}{{\text{O}}_{\text{2}}}}} = x{\text{mmHg}}$
We know that the given gases form a non-reactive gaseous mixture. So using the Dalton’s law of partial pressures for the given mixture, we get,
${{\text{P}}_{\text{T}}} = {{\text{p}}_{{{\text{N}}_{\text{2}}}}} + {{\text{p}}_{{\text{He}}}} + {{\text{p}}_{{\text{Ar}}}} + {{\text{p}}_{{\text{C}}{{\text{O}}_2}}}$
Substituting the values, we get,
$987 = 44.0 + 466 + 220 + x$
$\Rightarrow x = 987 - \left( {44 + 466 + 220} \right)$
Solving this, we get:
$\therefore x = 252\;{\text{torr}}$
We know that,
$1{\text{ torr}} = \dfrac{1}{{760}}{\text{atm}}$.
Thus, $252{\text{torr}} = \dfrac{{252}}{{760}}{\text{atm}} = 0.338{\text{atm}}$
The partial pressure of carbon dioxide in the given gaseous mixture is $0.338{\text{ atm}}$.

Thus, the correct option is C.

Note:
On the basis of the kinetic theory of gases, we know that a gas diffuses in a container to fill up the entire volume of the container and there are no forces of attraction between the molecules of a gas. In simpler terms, the different molecules in a mixture of gases act independently. So we can conclude that each gas in a mixture of gases exerts its own pressure on the system, which are then added up to get the total pressure of the mixture of gases in a container. This is given by the relation,
${{\text{P}}_{\text{T}}} = {{\text{p}}_{\text{1}}} + {{\text{p}}_{\text{2}}} + ........{{\text{p}}_{\text{n}}}$