Question

At low pressure, the graph of $PVvs{\displaystyle \frac{1}{V}}$.for a given amount at a constant temperature for a real gas is:
A. straight line parallel to x axis
B. straight line having positive intercept and negative slope
C. straight line passing through origin having positive slope
D. none of the above

Answer 1

Hint: At low pressure, $PV=RT-{\displaystyle \frac{a}{V}}$ at a constant temperature for a real gas. Here –a represents the slope and RT represents the intercept of a $PVvs{\displaystyle \frac{1}{V}}$. And the graph of $PVvs{\displaystyle \frac{1}{V}}$ is of straight line.

Complete step by step solution:
From your chemistry lessons you have learned about the real gas and the graph of $PVvs{\displaystyle \frac{1}{V}}$ at a constant temperature for a real gas where pressure is low. Real gases are gases that do not follow the ideal relation with gas laws. The deviation of the real gas from the ideal gas behavior is because of the assumptions that, if the pressure will increase then the volume will decrease. The value of volume can be smaller but not be zero because molecules of gases will occupy some of the space and we cannot compress that space further. Now, at high pressure the measured value of volume is more than that of calculated volume while at low pressure the values of measured and calculated volume will approach each other at the constant temperature. In the question we have to plot the graph of $PVvs{\displaystyle \frac{1}{V}}$ at low pressure and at constant temperature of a real gas. So, at low pressure the relation between PV and ${\displaystyle \frac{1}{V}}$ is given as:
$$PV=RT-{\displaystyle \frac{a}{V}}$$
Here we can see that this equation ressembel the equation of a straight line that is y=mx+c where m is the slope and C is the intercept at Y axis. Now if we write the equation (i) in the form of straight line it is written as:
$$PV=-{\displaystyle \frac{a}{V}}+RT$$
So, the slope will be –a and the intercept will be RT. Therefore the graph will be of straight line with negative slope and positive intercept.

Thus the correct option will be (B).

Note: Real gas does not follow any gaseous law like Boyle's law, Charles law, Avagadro law perfectly under all the conditions of pressure and temperature. Ideal gases are also called as perfect gas and the equation of ideal gases are PV=nRT. It gives the relation between the four different variables such as pressure, volume, temperature and moles.