Question

Gram molecular volume of oxygen at STP is:
A. $3200{\text{ c}}{{\text{m}}^3}$
B. $5600{\text{ c}}{{\text{m}}^3}$
C. $22400{\text{ c}}{{\text{m}}^3}$
D. $11200{\text{ c}}{{\text{m}}^3}$

Answer 1

Hint: Gram molecular volume of a gas is also known as molar volume of a gas and Gram molecular volume of any ideal gas at STP is fixed and it can be calculated by using the ideal gas equation.

Complete step by step answer:
Volume of one mole of a gas is known as gram molecular volume or molar volume of gas. Molar volume of any ideal gas depends upon pressure and temperature conditions. STP is the abbreviation for standard temperature and pressure in which standard pressure is 1 atm and standard temperature is 273.15 K. Molar volume of any ideal gas can be calculated by using ideal gas phase equation, which is as
$PV = nRT$.
Here P is the pressure of the gas, V is the volume of gas, n is number of moles of gas, T is the absolute temperature of gas and R is the universal gas constant.
Given: moles of oxygen gas ${\text{n = 1}}$mol, for STP, ${\text{P = 1}}$atm, $T{\text{ = 273}}{\text{.15}}K$ and $R{\text{ = 0}}{\text{.0821 L}}{\text{.atm}}{\text{.mo}}{{\text{l}}^{ - 1}}{K^{ - 1}}$.
By substituting values of P, n, T and R in ideal gas phase equation, we will get,
$1{\text{ x V = 1 x 0}}{\text{.0821 x 273}}{\text{.15}} {\text{V = 22}}{\text{.4 L}}$
Since $1{\text{ L = 1000 c}}{{\text{m}}^3}$.
So,$V{\text{ = 22400 c}}{{\text{m}}^3}$.

Hence, gram molecular volume of oxygen gas at STP is $22400{\text{ c}}{{\text{m}}^3}$ and the correct option is (C).

Note: The value of pressure, temperature, moles and R should be taken with a proper unit system. The value of universal gas constant (R) should be taken with similar units as of pressure and volume. Value of the number of moles will be 1 mol for calculation of molar volume or gram molecular volume of gas. Here oxygen gas is assumed as an ideal gas.