Question

One mole of a non-ideal gas undergoes a change of state $(2.0 atm, 3.0L, 95K)$ $ \to $ $(4.0 atm, 5.0L, 245K)$ with a change in internal energy, $\Delta {\text{U}}$ = $30L-atm$. The change in enthalpy of the process in L-atm is:
A. $40.0$
B. $42.3$
C. $44.0$
D. None of these

Answer 1

Hint:A gas is called non-ideal in chemistry when it does not follow the ideal gas equation or the gas laws under a wide range of temperature and pressure. And internal energy is defined as the energy produced due to the randomness of the particles, molecules present in a thermodynamic system.

Formula used:$\Delta {\text{H}}$ = $\Delta {\text{U + }}\Delta {\text{PV}}$
Where, $\Delta {\text{H}}$ = Change in enthalpy, $\Delta {\text{U}}$ = change in internal energy, $\Delta {\text{PV}}$ = Change in the pressure and volume of the gas.

Complete step-by-step solution:
In this question, we are given all the required values of the terms which are required for us to get to our solution, so let’s start solving;First, we will calculate the value of change in pressure and volume ($\Delta {\text{PV}}$) as the direct value is not given, for this, we will use the given two values of pressure and volume.
$ \Rightarrow $$\Delta {\text{PV}}$ = ${{\text{P}}_2}{{\text{V}}_2} - {{\text{P}}_1}{{\text{V}}_1}$
$ \Rightarrow $$\Delta {\text{PV}}$ = $4 \times 5{\text{ }} - {\text{ }}3 \times 2$
$ \Rightarrow $$\Delta {\text{PV}}$ = $20 - 6$
$ \Rightarrow $$\Delta {\text{PV}}$ = $14$
Now let’s put all the values in the mentioned formula,
$ \Rightarrow $$\Delta {\text{H}}$ = $\Delta {\text{U + }}\Delta {\text{PV}}$
$ \Rightarrow $$\Delta {\text{H}}$ = $30 + 14$
$ \Rightarrow $$\Delta {\text{H}}$ =$ 44.0$
Therefore, the change in enthalpy of the system after the non-ideal gas changes its states is $44.0$

Hence, the correct answer is option (C) i.e. $44.0$

Note:Although the solution to the question seems easy but remember when we are using the term internal energy of a system we are not talking about the all energy present in the system, the total energy of the system depends upon the kinetic and the potential energy of the system and is denoted by E.