Question

If at NTP the volume of a gas is $40mL$ . Calculate the volume of gas when the pressure is increased to $800mm$ of Hg at the same temperature.
(A) $38mL$
(B) $22400mL$
(C) $240mL$
(D) $431mL$

Answer 1

The variation of volume and pressure without the variation of temperature can be correlated according to Boyle’s law which states that “the volume of an ideal gas is inversely proportional to its pressure at a given temperature”. This law will be used to solve the given problem.
Formula used:
We can write the expression for Boyle’s law as,
${P_1}{V_1} = {P_2}{V_2}$
In this equation the different quantities can be described as,
${P_1} = {\text{initial pressure of the given gas}} \\\ {P_1} = {\text{final pressure of the given gas}} \\\ {V_1} = {\text{initial volume of the given gas}} \\\ {V_2} = {\text{final volume of the given gas}} \\\$

Complete step by step answer:
$1.$ Here the quantities given to us are,
Initial pressure of gas, ${P_1} = 760mm{\text{ of Hg}}$
Final pressure of gas, ${P_2} = 800mm{\text{ of Hg}}$
Initial volume of gas, ${V_1} = 40mL$
Final volume of gas, ${V_2} = {\text{ to be calculated}}$
$2.$ On applying the formula we can write,
${P_1}{V_1} = {P_2}{V_2}$
$760 \times 40 = 800 \times {V_2} \\\ {V_2} = \dfrac{{760 \times 40}}{{800}} \\\ {V_2} = 38mL \\\$
So, the final volume of the gas comes out to be $38mL$. Hence, our final answer is option ‘A’.
Additional information: The behavior of gases is governed by different gas laws which relate the pressure, temperature and volume of ideal gases. These are Charle’s law, Boyle’s law and Gay-Lussac’s law. Boyle’s law is named after the scientist ‘Robert Boyle’. The combined law also called as combined gas law of all the three gas laws can be written as:
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
It is interesting to know that these gas laws do not apply to real gases.

Note:
On attempting these type of questions three things to be remembered are (i) always use the same units of all the quantities for example in this question the volume and pressure have the same units, (ii) at NTP (normal temperature and pressure) the temperature is $273.5K$ and pressure is $1{\text{ atmosphere or 760 mm of Hg}}$ and (iii) consider the gas as ideal gas unless given.