Question

A graph is plotted with $PV/T$ on $y-$ axis and mass of the gas along $x-$ axis for different gases. The graph is

• A. a straight line parallel to $x-$ axis for all the gases.
• B. a straight line passing through origin with a slope having a constant value for all the gases.
• C. a straight line passing through origin with a slope having different values for different gases.
• D. a straight line parallel to $y-$ axis for all the gases.

Answer 1

The correct option is C a straight line passing through origin with a slope having different values for different gases.

We know that,
$PV=nRT$
$\Rightarrow PV=\frac{m}{M}RT$, where $m$ is mass of the gas and $M$ is molar mass.
$\Rightarrow \frac{PV}{T}=\frac{R}{M}m$ ........(1)
On comparing (1) with the equation of a straight line, $y=m_{o}x+c$
where $y=\frac{PV}{T}$ & $x=m$
We get, $\text{y-intercept},c=0$
$\text{Slope},m_o=\frac{R}{M}$
As y-intercept is zero, the straight line passes through the origin.
Also, slope will be different for different gases as molar mass will be different.