Question

Suppose NTP is used in place of STP. What will be the change in molar volume of a gas if the new condition is defined by doubling the temperature as well as the pressure?
A. Molar volume will remain unchanged
B. Molar volume will become half
C. Molar volume will double itself
D. Molar volume will become $0.54$ times the earlier one

Answer 1

NTP refers to normal temperature and pressure. At NTP the temperature is ${25^0}C$ and the pressure is $1atm$ . In order to find out the new molar volume after doubling the temperature as well as pressure we have to take the ratio of both the molar volumes.

Complete answer:
As we know normal temperature and pressure conditions are ${25^0}C$ and $1atm$.
So, as $PV = nRT$
Where, $P$ = Pressure
$V$ = Volume
$n$ = number of moles
$T$ = temperature
$R$ = Gas constant
We can write it like: $V = \dfrac{{n \times R \times T}}{P}$
So, molar volume at normal temperature and pressure is:
$V = \dfrac{{1 \times R \times 298}}{1}$
Now, according to the question;
The temperature and pressure are doubled. So, new volume will be:
$V' = \dfrac{{1 \times R \times 323}}{2}$
Now, by dividing both the molar volume we will get:
$\dfrac{V}{{V'}} = \dfrac{1}{{0.54}}$
That is: $V' = 0.54V$
As new molar volume is $0.54$ times the volume at normal temperature and pressure condition.

Hence, option D is correct.
Additional information:
STP, which is standard temperature and pressure condition, is a reference which is used for the molar volume of an ideal gas. Hydrogen and helium are two gases which show positive deviation from ideal behavior at all pressure and $273K$ temperature. As are the lightest gases known. So, Their molecules have very small masses. So, the attractive forces between the molecules of these two gases are extensively small. So $a/{V^2}$ is negligible even at ordinary temperatures. Thus $PV > RT$ . Thus the Vander Waals equation describes the observed behaviour of real gases (quantitatively) and so it is an improvement over the ideal gas equation. At all temperatures, if the pressure is extremely high then there will be a positive deviation because of the size of the molecules.

Note:
According to Kinetic Molecular Theory, an increase in temperature results in an increase in the average kinetic energy of the molecules. As the particles move faster, they will collide to the edge of the container more often. If the reaction is kept at constant pressure, the particles must stay farther apart, and an increase in volume will compensate for the increase in particle collision with the surface of the container.