Question

If 500ml of a gas A at 1000 torr and 1000ml of gas B at 800 torr are placed in a 2L container, the final pressure will be (Suppose temperature is constant)-
A. 100 torr
B. 650 torr
C. 1800 torr
D. 2400 torr

Answer 1

Hint: There is a relationship between the number of moles, pressure, volume, temperature for a gas and it is as follows.
PV = nRT
Here, P = Pressure of the gas
V – Volume of the gas
n = number of moles of the gas
R = Gas constant
T = Temperature of the gas

Complete answer:
- In the question it is asked to calculate the final pressure of the gas having 500ml of a gas A at 1000 torr and 1000ml of gas B at 800 torr are placed in a 2L container.
- Initially we have to calculate the number of moles of the gases A and B and it is as follows.
Number of moles of gas ‘A’, n = $\dfrac{PV}{RT}=\dfrac{500\times 1000}{RT}$
Number of moles of gas ‘B’, $n'=\dfrac{PV}{RT}=\dfrac{1000\times 800}{RT}$
- Now by using the below formula we can calculate the final pressure of the gaseous mixture and it is as follows.
\[P=\dfrac{nRT}{V}\]
Here n = n+ n’
Then
\[\begin{align}
  & P=\dfrac{(n+n')RT}{V} \\
 & P=\dfrac{\dfrac{500\times 1000}{RT}+\dfrac{1000\times 800}{RT}}{2000}RT \\
 & P=650torr \\
\end{align}\]
- Therefore, the total pressure is 650 torr.

So, the correct option is B.

Note:
Without knowing the individual number of moles of the gas A and gas B we cannot calculate the pressure of the mixture of the gases. Therefore, first we have to calculate the number of moles of the individual gases.