Question

consider the reaction cl₂(g) + br₂(g) → 2 brcl(g) at 25 °c. using the information in the table, determine δs for this reaction. compound δs° (j/mol·k) cl₂ (g) 223 br₂ (g) 245.4 brcl (g) 240

Explanation:

Step1: Recall the formula for entropy change

The formula for the standard entropy change (\(\Delta S^\circ\)) of a reaction is \(\Delta S^\circ=\sum n\Delta S^\circ_{products}-\sum m\Delta S^\circ_{reactants}\), where \(n\) and \(m\) are the stoichiometric coefficients of products and reactants respectively.

Step2: Identify the stoichiometric coefficients and \(\Delta S^\circ\) values

For the reaction \(\ce{Cl2(g) + Br2(g) -> 2 BrCl(g)}\):

• Reactants: \(\ce{Cl2(g)}\) with \(m = 1\) and \(\Delta S^\circ=223\space J/mol\cdot K\); \(\ce{Br2(g)}\) with \(m = 1\) and \(\Delta S^\circ = 245.4\space J/mol\cdot K\)
• Product: \(\ce{BrCl(g)}\) with \(n = 2\) and \(\Delta S^\circ=240\space J/mol\cdot K\)

Step3: Calculate the entropy of products

The entropy of products is \(n\times\Delta S^\circ_{BrCl}=2\times240 = 480\space J/mol\cdot K\)

Step4: Calculate the entropy of reactants

The entropy of reactants is \(m_1\times\Delta S^\circ_{Cl2}+m_2\times\Delta S^\circ_{Br2}=1\times223 + 1\times245.4=223 + 245.4 = 468.4\space J/mol\cdot K\)

Step5: Calculate \(\Delta S^\circ\)

\(\Delta S^\circ=\) Entropy of products \(-\) Entropy of reactants \(=480-468.4 = 11.6\space J/mol\cdot K\)

Answer:

\(11.6\)