Question

A gas is collected in a graduated tube over mercury. The volume of the gas at ${25^\circ }C$ is $60mL$ and the level of mercury in the tube is $110mm$ above the mercury level. The barometer reads $760mm$. Volume of gas at STP is
(A) $33mL$
(B) $58mL$
(C) $39mL$
(D) $47mL$

Answer 1

Hint: As we are very well aware of gas laws including Boyle's law and Charles’ law that combine to give a relationship between the three variables which are pressure, temperature and volume.

Complete Step by step answer:
We know that gas laws are made to study the behaviour of gases which is much easier than solids and liquids. Boyle's law states that at constant temperature the pressure of a fixed amount of gas varies inversely with the volume of the gas and Charles’ law states that volume occupied by a given mass of gas is directly proportional to the absolute temperature of gas at constant pressure. When combined together these two laws gave a new relationship between the three variables which are pressure, temperature and volume. This is called combined gas law. This relationship of variables can be shown as:
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
In the question we are given with the initial volume ${V_1} = 60\;mL$, temperature ${T_1} = {25^\circ }C$ and pressure ${P_1} = 110\;mm$ and the barometer reading shows $P = 760\;mm$, so the effective pressure will be $ = 760 - 110 = 650\;mm$ which we will consider the ${P_1}$.

Now, at STP the variables should be changed according to stand pressure and temperature conditions so after converting we get:
${P_1} = 650\;torr$, ${V_1} = 60\;mL$and ${T_1} = 25 + 273 = {298^\circ }C$
Similarly, ${P_2} = 760\;torr$, ${T_2} = {273^\circ }C$and volume is to be calculated.

Applying the above formula we get:
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
$\Rightarrow \dfrac{{650 \times 60}}{{298}} = \dfrac{{760 \times {V_2}}}{{273}}$
On solving for ${V_2}$: ${V_2} = 47\;mL$.

Therefore the correct answer is (D).

Note: The volume of a given mass of gas increases with increase in temperature and decrease with decrease in temperature at a constant pressure. The absolute temperature is taken when the given temperature is added with ${273^\circ }C$ temperature, hence this temperature is also known as the kelvin temperature scale or thermodynamic scale of temperature. And the standard pressure we used is given as the $760\;mmHg = 760\;torr$.