Question

In which one of the following processes is ΔH = ΔE? A. 2HI(g) => H2(g) + I2(g) at atmospheric pressure. B. Two moles of ammonia gas are cooled from 325 ?°C to 300 °C at 1.2 atm. C. H2O(l) => H2O(g) at 100 °C at atmospheric pressure. D. CaCO3(s) => CaO(s) + CO2(g) at 800 °C at atmospheric pressure. E. CO2(s) => CO2(g) at atmospheric pressure.

Answer 1

Answer : Only option A shows
`\Delta H=\Delta E`

Explanation :

Formula used :

`\Delta H=\Delta E+\Delta n_gRT`

`\Delta H` = change in enthalpy

`\Delta E` = change in internal energy

`\Delta n_g` = change in moles

R = gas constant = 8.314 J/mol.K

T = temperature

According to the question,
`\Delta H=\Delta E` when the value of
`\Delta n_gRT` will be zero.

Now we have to determine the value of
`\Delta n_gRT` for the following cases.

(A)
`2HI(g)\rightarrow H_2(g)+I_2(g)` at atmospheric pressure.

In this case:

`\Delta n_g` = change in moles

Change in moles = Number of moles of product side - Number of moles of reactant side

According to the reaction:

Change in moles = (1+1) - 2 = 2 - 2 = 0 mole

That means, value of
`\Delta n_gRT` = 0

So, in this process
`\Delta H=\Delta E`

(B) Two moles of ammonia gas are cooled from 325 °C to 300 °C at 1.2 atm.

In this case:

`\Delta n_g` = change in moles = 2

That means, value of
`\Delta n_gRT` ≠ 0

So, in this process
`\Delta H\\eq \Delta E`

(C)
`H_2O(l)\rightarrow H_2O(g)` at 100 °C at atmospheric pressure.

In this case:

Change in moles = Number of moles of product side - Number of moles of reactant side

According to the reaction:

Change in moles = 1 - 0 = 1 mole

`\Delta n_g` = change in moles = 1

That means, value of
`\Delta n_gRT` ≠ 0

So, in this process
`\Delta H\\eq \Delta E`

(D)
`CaCO_3(s)\rightarrow CaO(s)+CO_2(g)` at 800 °C at atmospheric pressure.

In this case:

Change in moles = Number of moles of product side - Number of moles of reactant side

According to the reaction:

Change in moles = 1 - 0 = 1 mole

`\Delta n_g` = change in moles = 1

That means, value of
`\Delta n_gRT` ≠ 0

So, in this process
`\Delta H\\eq \Delta E`

(E)
`CO_2(s)\rightarrow CO_2(g)` at atmospheric pressure.

In this case:

Change in moles = Number of moles of product side - Number of moles of reactant side

According to the reaction:

Change in moles = 1 - 0 = 1 mole

`\Delta n_g` = change in moles = 1

That means, value of
`\Delta n_gRT` ≠ 0

So, in this process
`\Delta H\\eq \Delta E`

Hence, from this we conclude that, only option A shows
`\Delta H=\Delta E`