Question

Which of the following equations shows the relationship between heat of reaction at constant pressure and heat of reaction at constant volume if the temperature is not constant?

• A. \( \Delta H - \Delta n = \Delta U RT \)
• B. \( \Delta H - \Delta U = \Delta n RT \)
• C. \( \Delta H = \Delta n RT \)
• D. \( \Delta H = \Delta U - RT \)

Hint:

Always remember: for gaseous reactions, \( \Delta H = \Delta U + \Delta nRT \).

Answer 1

The Correct Option is B

Step 1: Understanding thermodynamic terms.
At constant pressure, the heat of reaction is represented by enthalpy change \( \Delta H \), while at constant volume, it is represented by internal energy change \( \Delta U \). The difference between these two arises due to work done by gases during expansion or contraction.

Step 2: Relation between \( \Delta H \) and \( \Delta U \).
For reactions involving gases, the relationship between enthalpy change and internal energy change is given by:
\[ \Delta H = \Delta U + \Delta n RT \] where \( \Delta n \) is the change in number of moles of gaseous species.

Step 3: Rearranging the equation.
Rearranging the above expression, we get:
\[ \Delta H - \Delta U = \Delta n RT \]

Step 4: Conclusion.
Thus, the correct relationship between heat of reaction at constant pressure and constant volume is option (B).