Answered

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 :

Answer : Only option A shows [tex]\Delta H=\Delta E[/tex]

Explanation :

Formula used :

[tex]\Delta H=\Delta E+\Delta n_gRT[/tex]

[tex]\Delta H[/tex] = change in enthalpy

[tex]\Delta E[/tex] = change in internal energy

[tex]\Delta n_g[/tex] = change in moles

R = gas constant = 8.314 J/mol.K

T = temperature

According to the question, [tex]\Delta H=\Delta E[/tex] when the value of [tex]\Delta n_gRT[/tex] will be zero.

Now we have to determine the value of [tex]\Delta n_gRT[/tex] for the following cases.

(A) [tex]2HI(g)\rightarrow H_2(g)+I_2(g)[/tex] at atmospheric pressure.

In this case:

[tex]\Delta n_g[/tex] = 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 [tex]\Delta n_gRT[/tex] = 0

So, in this process [tex]\Delta H=\Delta E[/tex]

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

In this case:

[tex]\Delta n_g[/tex] = change in moles = 2

That means, value of [tex]\Delta n_gRT[/tex] ≠ 0

So, in this process [tex]\Delta H\neq \Delta E[/tex]

(C) [tex]H_2O(l)\rightarrow H_2O(g)[/tex] 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

[tex]\Delta n_g[/tex] = change in moles = 1

That means, value of [tex]\Delta n_gRT[/tex] ≠ 0

So, in this process [tex]\Delta H\neq \Delta E[/tex]

(D) [tex]CaCO_3(s)\rightarrow CaO(s)+CO_2(g)[/tex] 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

[tex]\Delta n_g[/tex] = change in moles = 1

That means, value of [tex]\Delta n_gRT[/tex] ≠ 0

So, in this process [tex]\Delta H\neq \Delta E[/tex]

(E) [tex]CO_2(s)\rightarrow CO_2(g)[/tex] 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

[tex]\Delta n_g[/tex] = change in moles = 1

That means, value of [tex]\Delta n_gRT[/tex] ≠ 0

So, in this process [tex]\Delta H\neq \Delta E[/tex]

Hence, from this we conclude that, only option A shows [tex]\Delta H=\Delta E[/tex]

Other Questions