In which of the following processes is ΔH = ΔE?

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

b. One gram of water is vaporized at 100 °C and 1 atm.

c. Two moles of hydrogen iodide gas react to form hydrogen gas and iodine gas in a 40-L container.

d. Calcium carbonate is heated to form calcium oxide and carbon dioxide in a container with variable volume.

e. ΔH and ΔE are different in all these processes.

c. Two moles of hydrogen iodide gas react to form hydrogen gas and iodine gas in a 40-L container.

Explanation:

The enthalpy (ΔH) is related to the internal energy (ΔE) through the following expressions.

ΔH = ΔE + P.ΔV [1]

ΔH = ΔE + R. T.Δn (gas) [2]

where,

P is the pressure

ΔV is the change in the volume

R is the ideal gas constant

T is the absolute temperature

Δn (gas) is the change in the gaseous moles

When ΔV = 0 or Δn (gas) = 0, ΔH will be equal to ΔE.

In which of the following processes is ΔH = ΔE?

a. Two moles of ammonia gas are cooled from 325 °C to 300 °C at 1.2 atm. NO. When ammonia is cooled, the volume is decreased, that is, ΔV < 0 and ΔH ≠ ΔE.

b. One gram of water is vaporized at 100 °C and 1 atm. NO. The corresponding reaction is: H₂O (l) ⇒ H₂O (g). Δn (gas) = 1 - 0 = 1. Then, ΔH ≠ ΔE.

c. Two moles of hydrogen iodide gas react to form hydrogen gas and iodine gas in a 40-L container. YES. The container has a constant volume (ΔV = 0). Also, the corresponding reaction is: 2 HI (g) ⇄ H₂ (g) + I₂ (g). Δn (gas) = 2 - 2 = 0. Then, ΔH = ΔE.

d. Calcium carbonate is heated to form calcium oxide and carbon dioxide in a container with variable volume. NO. The corresponding reaction is: CaCO₃ (s) ⇒ CaO (s) + CO₂ (g). Δn (gas) = 1 - 0 = 1. Then, ΔH ≠ ΔE.