Question

A quantity of gas is collected in a graduated tube over mercury. The volume of the gas at ${20^ \circ }{\text{C}}$ is $50.0{\text{ mL}}$ and the level of mercury in the tube is $100{\text{ mm}}$ above the outside mercury level. The barometer reads $750{\text{ mm}}$. Volume at STP is:
A. $39.8{\text{ mL}}$
B. $40{\text{ mL}}$
C. $42{\text{ mL}}$
D. $60{\text{ mL}}$

Answer 1

Hint:We are given that the level of mercury in the tube is $100{\text{ mm}}$ above the outside mercury level and the barometer reading is $750{\text{ mm}}$. To find the level of mercury in the tube, subtract the given level from the barometer reading.

Complete answer:
We will first calculate the level of mercury in the tube. To find the level of mercury in the tube, subtract the given level from the barometer reading. The level in the tube is the measurement of pressure. Thus,
${P_1} = \left( {750 - 100} \right){\text{ mm}}$
$\Rightarrow {P_1} = 650{\text{ mm}}$
Thus, the volume of the gas is $650{\text{ mm}}$.
The temperature given is ${20^ \circ }{\text{C}}$. Thus,
${T_1} = {20^ \circ }{\text{C}} + 273$
$\Rightarrow {T_1} = 293{\text{ K}}$
And the volume of the gas is ${V_1} = 50.0{\text{ mL}}$.
We have to calculate the volume of gas at STP i.e. standard temperature and pressure.
The standard temperature and pressure means the temperature is $298{\text{ K}}$ and the pressure is $1{\text{ atm}}$.
Thus, ${T_2} = 273{\text{ K}}$ and ${P_2} = 1{\text{ atm}} = 760{\text{ mm}}$.
We know the ideal gas equation is,
$PV = nRT$
Where,
$P$ is the pressure of the ideal gas,
$V$ is the volume of the ideal gas,
$n$ is the number of moles of ideal gas,
$R$ is the universal gas constant,
$T$ is the temperature of the gas.
Thus,
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$
$\Rightarrow {V_2} = \dfrac{{{P_1}{V_1}{T_2}}}{{{T_1}{P_2}}}$
$\Rightarrow {V_2} = \dfrac{{650{\text{ mm}} \times 50.0{\text{ mL}} \times 273{\text{ K}}}}{{293{\text{ K}} \times 760{\text{ mm}}}}$
$\Rightarrow {V_2} = 39.8{\text{ mL}}$
Thus, the volume of gas at STP is $39.8{\text{ mL}}$.

Thus, the correct option is (A) $39.8{\text{ mL}}$.

Note:
Ideal gas is a hypothetical gas. The ideal gas molecules do not attract or repel each other. The ideal gas law states that the pressure, temperature and the volume of a gas are related to each other. The interaction between molecules of an ideal gas is elastic collision or elastic collision with the container walls.