Question

Work done during the combustion of one mole of $\mathrm{CH}_{4}$ in a bomb calorimeter is:

A. zero
B. $-101 , J$
C. $-24.2 , J$
D. $-1 , J$

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Answer

To solve the question of determining the work done during the combustion of one mole of $\mathrm{CH}_{4}$ (methane) in a bomb calorimeter, we need to focus on the nature of the process and any changes in volume. Here's a detailed solution:

Step-by-Step :

  1. Combustion Reaction:

    The combustion of methane ($ \mathrm{CH}{4} $) can be represented by the balanced chemical equation: $$ \mathrm{CH}{4}(g) + 2 , \mathrm{O}{2}(g) \rightarrow \mathrm{CO}{2}(g) + 2 , \mathrm{H}_{2}\mathrm{O}(l) $$

  2. Understanding the bomb calorimeter:

    • A bomb calorimeter is a device used to measure the heat of combustion of a substance.
    • The key aspect of a bomb calorimeter is that the reaction occurs at a constant volume (isochoric process).
  3. Work Done in a Constant Volume Process:

    • For a process occurring at constant volume, the work done ($ W $) is related to any volume change.
    • In a bomb calorimeter, since volume does not change ($ \Delta V = 0 $), the work done ($ W $) is given by: $$ W = -P \Delta V $$
    • Here, $ \Delta V = 0 $, so: $$ W = -P \times 0 = 0 $$
  4. Conclusion:

    Since the reaction occurs in a bomb calorimeter (constant volume), the work done during the combustion of one mole of $\mathrm{CH}_{4}$ is zero.

Final Answer:

A. zero

The work done during the combustion of one mole of methane in a bomb calorimeter is zero.


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