At \(25^{\circ} \mathrm{C}\), the enthalpy of the following processes are given: \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{OH}(\mathrm{g}) \Delta \mathrm{H}^{\mathrm{o}}=78 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \Delta \mathrm{H}^{\mathrm{o}}=-242 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(\mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g}) \Delta \mathrm{H}^{\mathrm{o}}=436 \mathrm{~kJ} \mathrm{~mol}^{-1}\) \(1 / 2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{O}(\mathrm{g}) \Delta \mathrm{H}^{\mathrm{o}}=249 \mathrm{~kJ} \mathrm{~mol}^{-1}\) What would be the value of X for the following reaction? ____ (Nearest integer) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{H}(\mathrm{g})+\mathrm{OH}(\mathrm{g}) \Delta \mathrm{H}^{\mathrm{o}}=\mathrm{X} \mathrm{kJ} \mathrm{mol}^{-1}\)

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Chemical Thermodynamics

2 5^{\circ} C

, the enthalpy of the following processes are given:

H_{2} (g) + O_{2} (g) \to 2 OH (g) Δ H^{o} = 78 kJ mol^{- 1}

H_{2} (g) + 1/2 O_{2} (g) \to H_{2} O (g) Δ H^{o} = - 242 kJ mol^{- 1}

H_{2} (g) \to 2 H (g) Δ H^{o} = 436 kJ mol^{- 1}

1/2 O_{2} (g) \to O (g) Δ H^{o} = 249 kJ mol^{- 1}

What would be the value of X for the following reaction? ____ (Nearest integer)

H_{2} O (g) \to H (g) + OH (g) Δ H^{o} = X kJ mol^{- 1}

Answer: 499

The target change

H_{2} O (g) \to H (g) + OH (g)

is assembled from the given data by Hess's law. Reversing

H_{2} + \frac{1}{2} O_{2} \to H_{2} O

contributes

+ 242 kJ mo l^{- 1}

; half of

H_{2} \to 2H

supplies one hydrogen atom at

+ 218 kJ mo l^{- 1}

; and half of

H_{2} + O_{2} \to 2OH

supplies one hydroxyl radical at

+ 39 kJ mo l^{- 1}

. Adding these, the hydrogen and oxygen cancel and leave exactly the required reaction, so

Δ H^{\circ} = 242 + 218 + 39

. The value of X is

499 kJ mo l^{- 1}

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer