Question

A gas occupies 200 ml at a pressure of 0.820 bar at ${20^0}C$ . How much volume will it
occupy when it is subjected to an external pressure of 1.025 bar at the same temperature? (Write value
to nearest integer)

Answer 1

We know the ideal gas equation $PV = nRT$ , in the given question there are only 2 variables Pressure and Volume.
And we know from Boyle’s Law that pressure and volume are inversely proportional, at constant
temperature.
So, we can derive relation between Pressure and Volume as:
$P\alpha \dfrac{1}{V}$

Complete step by step answer:
Ideal gas equation can be written as $PV = nRT$
And we know from Boyle’s Law that pressure and volume are inversely proportional at constant
temperature.
So, we can derive relation between Pressure and Volume at constant temperature (Isothermal condition)
as:
$P\alpha \dfrac{1}{V}$
To compare for same situation, different values of pressure and volume can be given by:
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{V_2}}}{{{V_1}}}$
Given Data:
The gas at the pressure of 0.82 bar occupies the volume of 200 ml.
$\therefore {P_1} = 0.82bar \\\ {V_1} = 200ml \\\$
So, now the external pressure is 1.025 bar, so we can calculate corresponding volume:
${P_2} = 1.025bar$
Using Equation,
$\dfrac{{{P_1}}}{{{P_2}}} = \dfrac{{{V_2}}}{{{V_1}}}$
Now substitute the given value in above equation:
$\dfrac{{0.82}}{{1.025}} = \dfrac{{{V_2}}}{{200}}$
Cross multiplying, and finding value of unknown variable volume,
$
\Rightarrow {V_2} = \dfrac{{0.82 \times 200}}{{1.025}} \\

\therefore {V_2} = 160ml \\
$
Thus the volume corresponding to external pressure of 1.025 bar is 160 ml (this value is perfect integer value).

Note:
Remember that pressure and volume are inversely proportional, so when one increases the other
decreases. Take complete note of all gas laws, and when to use which gas law is important, or else even
the general ideal gas equation could be used to come to conclusion of getting answer of any such related
quantity in the ideal gas equation.
Very important note, that no need to convert pressure into atmosphere for comparison purpose, and
even volume can be in ml, not required to be converted to litres. These quantities are not converted into
standard units as we just have to compare the values, which can be done even without conversion.