Question

If $∆\mathrm{H}$ is the change in enthalpy and $∆\mathrm{E}$ the change in internal energy accompanying a gaseous reaction?

• A. $∆\mathrm{H}$ is always greater than $∆\mathrm{E}$
• B. $∆\mathrm{H}<∆\mathrm{E}$ only if the number of moles of the products is greater than the number of the reactants
• C. $∆\mathrm{H}$ is always less than $∆\mathrm{E}$
• D. $∆\mathrm{H}<∆\mathrm{E}$ only if the number of moles of the products is less than the number of the reactants

Answer 1

The correct option is D

$∆\mathrm{H}<∆\mathrm{E}$ only if the number of moles of the products is less than the number of the reactants

Explanation for correct answer:-

Option D $∆\mathrm{H}<∆\mathrm{E}$ only if the number of moles of the products is less than the number of the reactants:-

We are aware that

$∆\mathrm{H}=∆\mathrm{E}+∆\left(\mathrm{PV}\right)$

where, $∆\mathrm{H}$ is the change in enthalpy

$∆\mathrm{E}$ is change in internal energy

Also, $\mathrm{PV}=\mathrm{nRT}$

Therefore,

$$\begin{gathered} ∆\mathrm{H}=∆\mathrm{E}+∆\left(\mathrm{PV}\right) \\ \mathrm{or}∆\mathrm{H}=∆\mathrm{E}+∆\left(\mathrm{nRT}\right) \end{gathered}$$

when there are fewer moles in the product than there are in the reactant.

So, $$\begin{gathered} ∆\mathrm{n}=-\mathrm{ve}[∆\mathrm{n}={\mathrm{n}}_{\mathrm{product}}-{\mathrm{n}}_{\mathrm{reactant}}] \\ \Rightarrow ∆\mathrm{H}<∆\mathrm{E} \end{gathered}$$

The correct answer is option D.

Explanation for incorrect answer :-

Option A $∆\mathrm{H}$ is always greater than $∆\mathrm{E}$

• It is not necessary $∆\mathrm{H}$ is always greater than $∆\mathrm{E}$. It can be seen in the above case Option A.
• Hence incorrect option.

Option B $∆\mathrm{H}<∆\mathrm{E}$ only if the number of moles of the products is greater than the number of the reactants

• when there are greater moles in the product than there are in the reactant then $∆\mathrm{H}>∆\mathrm{E}$.
• Hence incorrect option.

Option C $∆\mathrm{H}$ is always less than $∆\mathrm{E}$

• It is not necessary $∆\mathrm{H}$ is always less than $∆\mathrm{E}$. It can be seen in the above case option B.
• Hence incorrect option.

Final answer:- Hence, the correct answer is option D.