Question

If $500\;ml$ of gas A at $1000\;torr$, and $1000\;ml$ of gas B at $800\;torr$ are placed in a $2L$ container, the final pressure will be
A. $100\,torr$
B. $650\,torr$
C. $1800\,torr$
D. $2400\,torr$

Answer 1

Hint:We can use Dalton’s law of partial pressure here to solve the problem. It states that when a mixture of two or more non-reacting gases are enclosed in a container then the total pressure exerted by the gaseous mixture is equal to the sum of partial pressure of the individual gases.

Complete step by step solution:
From the hint we understood what Dalton's law of partial pressure was.
So, the mathematical expression for this is,
${{\text{P}}_{{\text{total}}}} = {{\text{P}}_1} + {{\text{P}}_2}$
Where ${{\text{P}}_{{\text{total}}}}$ is total pressure exerted
${{\text{P}}_1}$ and ${{\text{P}}_2}$ are the partial pressure of gases
We know that from the Ideal gas equation,
$PV = nRT$
Where $P$ is the pressure
$V$ is the volume
$n$ is the number of moles
$R$ is universal gas constant
$T$ is the temperature
Here, we are assuming that the temperature remains constant.
Then, we can write it as
${P_{total}} = \dfrac{{{n_{total}}RT}}{{{V_{total}}}}$
Where ${n_{total}}$ is the total number of moles of gases.
Since the total number of moles in the container will be equal to the sum of individual number of moles we can write
${n_{total}} = {n_1} + {n_2}$
Where ${n_1}$ and ${n_2}$ are the number of moles of individual gases.
And ${V_{total}} = 2L$ is given
Now we have to find ${n_1}$ and ${n_2}$
Applying the ideal gas law here we get
$\Rightarrow {n_1} = \dfrac{{{P_1}{V_1}}}{{RT}}$ and ${n_2} = \dfrac{{{P_2}{V_2}}}{{RT}}$
Substituting the values in ${P_{total}}$
$\Rightarrow {P_{total}} = \dfrac{{\left( {\dfrac{{{{\text{P}}_1}{{\text{V}}_1}}}{{{\text{RT}}}} + \dfrac{{{P_2}{V_2}}}{{RT}}} \right)RT}}{{{V_{total}}}} = \dfrac{{{P_1}{V_1} + {P_2}{V_2}}}{{{V_{total}}}}$
It is given that,
${P_1} = 500\,ml\,\;and\;\,{V_1} = 1000\,torr$
And ${P_2} = 1000\,ml\;and\;{V_2} = 800\,torr$
${V_{total}} = 2L = 2000\,ml$
Substituting these values we get,
$\Rightarrow {P_{total}} = \dfrac{{500 \times 1000 + 1000 \times 8000}}{{2000}}$
$ \Rightarrow {P_{total}} = 650\,torr$

Therefore the final pressure will be $650 \,torr$ i.e., option (b) is correct

Note:
If the temperature is constant, we can modify the ideal equation to
$\dfrac{{{P_1}{V_1}}}{{{n_1}}} = \dfrac{{{P_2}{V_2}}}{{{n_2}}}$
Where $P$, $V$ and $n$ are all the same as mentioned above.