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.

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