The figure shows plot of PV/T versus P for 1.00 \times 10^{-3} \mathrm{~kg} of oxygen gas at two different temperatures.
The figure shows plot of PV/T versus P for 1.00 \times 10^{-3} \mathrm{~kg} of oxygen gas at two different temperatures.

(a) What is the value of PV/T where the curves meet on the y-axis?

(b) If we obtained similar plots for 1.00 \times 10^{-3} kg of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot)? (Molecular mass of \mathrm{H}_{2}=2.02 \mathrm{u}, of \left.\mathrm{O}_{2}=32.0 \mathrm{u}, \mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} .\right)

Solution:

(a) We will use \mathrm{PV}=\mathrm{nR} \mathrm{T}

\mathrm{PV} / \mathrm{T}=\mathrm{nR}

Mass of the gas is given as =1 \times 10^{-3} \mathrm{~kg}=1 \mathrm{~g}

Molecular mass of \mathrm{O}_{2} is given as 32 \mathrm{~g} / \mathrm{mol}

So,

Number of mole = given weight / molecular weight

=1 / 32

So, n R=1 / 32 \times 8.314=0.26 \mathrm{~J} / \mathrm{K}

So,

Value of \mathrm{PV} / \mathrm{T}=0.26 \mathrm{~J} / \mathrm{K}

(b) 1 \mathrm{~g} of \mathrm{H}_{2} does not represent the same number of mole.

For Example, molecular mass of \mathrm{H}_{2} is 2 \mathrm{~g} / \mathrm{mol}

So, number of moles of \mathrm{H}_{2} require is 1 / 32

Therefore,

Mass of \mathrm{H}_{2} required = no. of mole of \mathrm{H}_{2} \times molecular mass of \mathrm{H}_{2}

\begin{array}{l} =1 / 32 \times 2 \\ =1 / 16 \mathrm{~g} \\ =0.0625 \mathrm{~g} \\ =6.3 \times 10^{-5} \mathrm{~kg} \end{array}

As a result, 6.3 \times 10^{-5} \mathrm{~kg} of \mathrm{H}_{2} would yield the same value