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# If ${S^o}$ for ${H_2},C{l_2}$ and $HCl$ are 0.13, 0.22 and 0.19 $kJ{K^{ - 1}}mo{l^{ - 1}}$ respectively. The total change in standard entropy for the reaction${H_2} + C{l_2} \to 2HCl$ is:A) $30J{K^{ - 1}}mo{l^{ - 1}}$ B) $40J{K^{ - 1}}mo{l^{ - 1}}$ C) $60J{K^{ - 1}}mo{l^{ - 1}}$ D) $20J{K^{ - 1}}mo{l^{ - 1}}$

Last updated date: 20th Sep 2024
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Hint: We are given the standard entropy values for ${H_2},C{l_2}$ and $HCl$. The total change in standard entropy for any reaction is the difference between standard entropy for products and standard entropy for reactants.

Complete step by step solution:
Let us first write the given values in the question.
Standard entropy for ${H_2}$ ($S_{{H_2}}^o$)= 0.13 $kJ{K^{ - 1}}mo{l^{ - 1}}$.
Standard entropy for $C{l_2}$ ($S_{C{l_2}}^o$) = 0.22 $kJ{K^{ - 1}}mo{l^{ - 1}}$.
Standard entropy for HCl ($S_{HCl}^o$) = 0.19 $kJ{K^{ - 1}}mo{l^{ - 1}}$.
Given reaction is: ${H_2} + C{l_2} \to 2HCl$
To find total change in standard entropy for the above reaction, we need to take the difference of the sum of standard entropy for products and sum of standard entropy for reactants.
Thus, we can also write, total change in standard entropy ($\Delta {S^o}$) as:$\Delta {S^o} = \sum n{S^o}({\text{products}}) - \sum n{S^o}({\text{reactants}})$
Here, n is the stoichiometric coefficient before products and reactants.
In the given reaction, the product is HCl and ${H_2}$and $C{l_2}$ are reactants.
Therefore, total change in standard entropy for the given reaction = $2(S_{HCl}^o) - (S_{{H_2}}^o + S_{C{l_2}}^o)$ . (Here, 2 is the stoichiometric coefficient of HCl).
Total change in standard entropy for the given reaction = $2(0.19) - (0.13 + 0.22) = 0.03KJ{K^{ - 1}}mo{l^{ - 1}} = 30J{K^{ - 1}}mo{l^{ - 1}}$ .

Thus, option A is the correct answer.

Note: It should be known that entropy change for a chemical reaction can be determined if standard or absolute entropies of each substance are known. The standard entropy of a substance is given by the symbol ${S^o}$and this is determined under standard conditions which are called STP conditions. The SI units for entropy are ${K^{ - 1}}mo{l^{ - 1}}$. As the temperature of the substance increases, its entropy increases because of an increase in the randomness of the molecules within the system.