Question

If $1$ litre of gas A is $600mm$ and of a gas B at $800mm$ are taken in a $2L$ bulb. The resulting pressure is:
A.1500mm \\\ B.1000mm \\\ C.2000mm \\\ D.500mm \\\

Answer 1

Hint : In order to solve this question, we first take the ratio of PV and RT from the first gas that is A and then similarly take the number of moles of gas B by taking ratios. Then for the total number of moles , we add them and equate it to the final ratio of PV by RT . Since the final volume is given we can get the final pressure.

Complete Step By Step Answer:
In the given question,
For gas A,
P = 600mm \\\ V = 1L \\\
Now the number of moles of A is equal to the pressure volume divided by the product of R and T.
So,
= \dfrac{{PV}}{{RT}} \\\ = \dfrac{{600 \times 1}}{{RT}} \\\ = \dfrac{{600}}{{RT}} \\\
Now coming on gas B,
Pressure is equal to $800mm$ .
Volume B is equal to $0.5L$ .
Now number of moles of B is equal to,
= \dfrac{{PV}}{{RT}} \\\ = \dfrac{{800 \times 0.5}}{{RT}} \\\ = \dfrac{{400}}{{RT}} \\\
Now the total number of moles here is equal to the moles of gas A to moles of gas B.
Here,
= \dfrac{{600}}{{RT}} + \dfrac{{400}}{{RT}} \\\ = \dfrac{{1000}}{{RT}} \\\
Simply, taking these fore final pressure and volume, we can also write as;
$\Rightarrow \dfrac{{{P_{final}}{V_{final}}}}{{RT}} = \dfrac{{1000}}{{RT}}$
Final volume will be given as;
${V_{final}} = 2L$
So,
{P_{final}} \times 2 = 1000 \\\ \Rightarrow {P_{final}} = 500mm \\\
Hence, D is the correct answer.

Note :
At the given constant pressure and temperature the volume of as gas is directly proportional to the number of moles of the gas.
Also at constant temperature and volume the pressure of a gas is directly proportional to the number of moles of the gas.
This is $PV = nRT$ .
Since, the final volume is given we can get the final pressure.