Question

Calculate the number of degrees of freedom of molecules of hydrogen in $1 \,cc$ of hydrogen gas at NTP.

• A. $2.344 \times 10^{16}$
• B. $1.344 \times 10^{20}$
• C. $2.124 \times 10^{21}$
• D. $4.212 \times 10^{20}$

Answer 1

Answer: (B)

Total number of degrees of freedom in a thermodynamical system $=$ number of degrees of freedom associated per molecule $x$ number of molecules,
As given molecules are of hydrogen.
$\therefore$ Volume occupied by $1$ mole
$=1$ mole of the gas at NTP
$=22400\, mL =22400 \,cc$
Any ideal gas has a molar volume of $22400 \,mL$ (cc) at NTP.
$\therefore$ Number of molecules in $1 \,cc$ of hydrogen
$=\frac{6.023 \times 10^{23}}{22400}=2.688 \times 10^{19}$
$H _{2}$ is a diatomic gas, having a total of $5$ degrees of freedom ( $3$ translational $+2$ rotational)
$\therefore$ Total degrees of freedom possessed by all the molecules $=5 \times 2.688 \times 10^{19}=1.344 \times 10^{20}$