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Which is not the correct relation between enthalpy \[\left( {\Delta {\text{H}}} \right)\] and intrinsic energy \[\left( {\Delta {\text{E}}} \right)\]
A.\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{P}}\Delta {\text{V}}\]
B.\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{nRT}}\]
C.\[\Delta {\text{H}} = \Delta {\text{E}} - {\text{P}}\Delta {\text{V}}\]
D.\[\Delta {\text{E}} = \Delta {\text{H}} - {\text{P}}\Delta {\text{V}}\]

Last updated date: 18th Jun 2024
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Hint: To answer this we must know the relation between enthalpy and intrinsic energy. Rearranging the formula will give us the above mentioned options; one of them is incorrectly represented. Take the help of the ideal gas equation.
Formula used: \[\Delta {\text{H}} = \Delta {\text{E}} + {\text{P}}\Delta {\text{V}}\]
Here Enthalpy is \[\left( {\Delta {\text{H}}} \right)\] and intrinsic energy or internal energy is \[\left( {\Delta {\text{E}}} \right)\] , P is pressure and V is volume.

Complete step by step answer:
The actual relationship between the enthalpy and the energy is as follow:
\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{P}}\Delta {\text{V}}\]
So, the given relation in option A stands correct.
Now if we rearrange the formula by moving the factor \[{\text{P}}\Delta {\text{V}}\] to the enthalpy side. We need to put the negative sign before \[{\text{P}}\Delta {\text{V}}\] . The equation will become:
\[\Delta {\text{E}} = \Delta {\text{H}} - {\text{P}}\Delta {\text{V}}\]
This is the same as the option D. So option D is also correct.
We know the ideal gas equation. The ideal gas equation says that:
\[{\text{P}}\Delta {\text{V}} = {\text{nRT}}\]
We can substitute the value of \[{\text{P}}\Delta {\text{V}}\] in the main formula. We will get the following equation:
\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{nRT}}\]
Hence, the given option B is correct.
There is no possible arrangement in which we can get the option C. Hence it is incorrect representation.

Thus, the correct option is C.

Enthalpy is defined as the sum of internal energy and product of pressure and volume. The heat absorbed or released in a system at constant pressure is known as enthalpy change. The energy present or stored within a substance is known as internal energy. Internal energy is a state function and is an extensive quantity. This means it depends upon the quantity of material and not on the nature. The negative of \[{\text{P}}\Delta {\text{V}}\] is known as work done in thermodynamics.