Example 5.9: Another Example of the Measurement of an Enthalpy Change
A gummy bear contains
2.67 g sucrose,
\(\ce{C12H22O11}\). When it reacts with
7.19 g potassium chlorate,
\(\ce{KClO3}\),
43.7 kJ of heat are produced. Determine the enthalpy change for the reaction
\(\ce{C12H22O11(aq)}\)\(\ce{ + }\)\(\ce{8KClO3(aq)}\)\(\ce{->}\)\(\ce{12CO2 (g)}\)\(\ce{ + }\)\(\ce{11H2O(l)}\)\(\ce{ + }\)\(\ce{8KCl(aq)}\)\(\ce{ }\)
Solution
\(m_{\mathrm{sucrose}}\) \(= 2.67\ \mathrm{g}\)
\(m_{\mathrm{\ce{KClO3}}}\) \(= 7.19\ \mathrm{g}\)
\(q_{\mathrm{rxn}}\) \(= -43.7\ \mathrm{kJ}\)
\(ΔH_{\mathrm{rxn}}\) = ?
Plan
1) How much reacts,
\(n_{\mathrm{\ce{->}}}\) 2)
\(ΔH_{\mathrm{rxn}}\) based on
\(n_{\mathrm{\ce{->}}}\)
\(n_{\mathrm{sucrose}}\) \(= \dfrac{m_{\mathrm{sucrose}}}{M_{\mathrm{\ce{C12H22O11}}}}\)
\(\ \ \ =\dfrac{2.67\ \mathrm{g}}{342.30\ \frac{\mathrm{g}}{\mathrm{mol}}}\)
\(\ \ \ =7.80\times 10^{-3}\ \mathrm{mol}\)
\(ν_{\mathrm{sucrose}}\) \(= 1\)
\(n_{\mathrm{\ce{KClO3}}}\) \(= \dfrac{m_{\mathrm{\ce{KClO3}}}}{M_{\mathrm{\ce{KClO3}}}}\)
\(\ \ \ =\dfrac{7.19\ \mathrm{g}}{122.55\ \frac{\mathrm{g}}{\mathrm{mol}}}\)
\(\ \ \ =0.05867\ \mathrm{mol}\)
\(ν_{\mathrm{\ce{KClO3}}}\) \(= 8\)
\(n_{\mathrm{\ce{->}}}\) \(= \mathrm{min}(\dfrac{n_{\mathrm{sucrose}}}{ν_{\mathrm{sucrose}}}, \dfrac{n_{\mathrm{\ce{KClO3}}}}{ν_{\mathrm{\ce{KClO3}}}})\)
\(\ \ \ =\mathrm{min}(\dfrac{7.80\times 10^{-3}\ \mathrm{mol}}{1}, \dfrac{0.05867\ \mathrm{mol}}{8})\)
\(\ \ \ =\mathrm{min}(7.800\times 10^{-3}\ \mathrm{mol}, 7.334\times 10^{-3}\ \mathrm{mol})\)
\(\ \ \ =7.33\times 10^{-3}\ \mathrm{mol}\)
\(ΔH_{\mathrm{rxn}}\) \(= \dfrac{q_{\mathrm{rxn}}}{n_{\mathrm{\ce{->}}}}\)
\(\ \ \ =\dfrac{-43.7\ \mathrm{kJ}}{7.33\times 10^{-3}\ \mathrm{mol}}\)
\(\ \ \ =-5.96\times 10^{3}\ \frac{\mathrm{kJ}}{\mathrm{mol}}\)
\(\ce{C12H22O11}\)\(\ce{ + }\)\(\ce{8KClO3}\)\(\ce{->}\)\(\ce{12CO2}\)\(\ce{ + }\)\(\ce{11H2O}\)\(\ce{ + }\)\(\ce{8KCl~~~~~~~~~ΔH~=~-5960kJ/mol}\)\(\ce{ }\)