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Consider the following reactions : (a...

Consider the following reactions :
(a) `H_((aq))^(+)+OH_((aq))^(-)=H_(2)O_((l)), Delta H= - X_(1)"kJ mol"^(-1)`
(b) `H_(2(g))+(1)/(2)O_(2(g))=H_(2)O_((l)), Delta H= - X_(2)"kJ mol"^(-1)`
(c ) `CO_(2(g))+H_(2(g))=CO_((g))+H_(2)O_((l))- X_(3)"kJ mol"^(-1)`
(d) `C_(2)H_(2(g))+(5)/(2)O_(2(g))=2CO_(2(g))+H_(2)O_((l))+X_(4)"kJ mol"^(-1)`
Enthalpy of formation of `H_(2)O_((l))` is :

A

`+X_(3) kJ mol^(-1)`

B

`-X_(-4) kJ mol^(-1)`

C

`+X_(1) kJ mol^(-1)`

D

`-X_(2) kJ mol^(-1)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the enthalpy of formation of water (H₂O(l)), we need to analyze the given reactions and identify which one corresponds to the formation of one mole of water from its constituent elements (hydrogen and oxygen). ### Step-by-Step Solution: 1. **Understanding Enthalpy of Formation**: - The enthalpy of formation (ΔH_f) of a compound is defined as the heat change that results when one mole of the compound is formed from its elements in their standard states. - For water (H₂O), the reaction must involve hydrogen gas (H₂) and oxygen gas (O₂) as reactants. 2. **Analyzing the Given Reactions**: - **Reaction (a)**: \[ H^+_{(aq)} + OH^-_{(aq)} \rightarrow H_2O_{(l)}, \Delta H = -X_1 \text{ kJ mol}^{-1} \] - This reaction involves ions and does not represent the formation of water from its elemental gases. Therefore, it is not applicable for ΔH_f of H₂O. - **Reaction (b)**: \[ H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O_{(l)}, \Delta H = -X_2 \text{ kJ mol}^{-1} \] - This reaction shows the formation of one mole of water from its elements, hydrogen and oxygen, in their standard states. This is exactly what we need for the enthalpy of formation of water. - **Reaction (c)**: \[ CO_2(g) + H_2(g) \rightarrow CO(g) + H_2O_{(l)}, \Delta H = -X_3 \text{ kJ mol}^{-1} \] - This reaction involves the formation of water but not from its elemental form. Therefore, it is not applicable for ΔH_f of H₂O. - **Reaction (d)**: \[ C_2H_2(g) + \frac{5}{2}O_2(g) \rightarrow 2CO_2(g) + H_2O_{(l)}, \Delta H = -X_4 \text{ kJ mol}^{-1} \] - Similar to reaction (c), this reaction produces water but does not involve its formation from elemental hydrogen and oxygen. Hence, it is not applicable for ΔH_f of H₂O. 3. **Conclusion**: - The only reaction that meets the criteria for the enthalpy of formation of water is **Reaction (b)**. Therefore, the enthalpy of formation of H₂O(l) is given by: \[ \Delta H_f = -X_2 \text{ kJ mol}^{-1} \] ### Final Answer: The enthalpy of formation of H₂O(l) is \(-X_2 \text{ kJ mol}^{-1}\).
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