Question 14.14: A 0.500-L sample of 0.200 M NaCl(aq) is added to 0.500 L of ......
A 0.500-L sample of 0.200 M NaCl(aq) is added to 0.500 L of 0.200 M AgNO_{3}(aq) in a calorimeter with a known total heat capacity equal to 4.60 × 10^{3}\ J·K^{−1} at a constant pressure of one bar. The observed temperature change is +1.423 K. Use these data to determine the value of ΔH^{\circ}_{rxn} for the equation
AgNO_{3}(aq) + NaCl(aq) → AgCl(s) + NaNO_{3}(aq)Stoichiometrically equivalent quantities of NaCl(aq) and AgNO_{3}(aq) are added to each other, and so there is no limiting reactant in this case. The observed increase in temperature arises from the formation of the precipitate AgCl(s). The number of moles of AgCl(s) formed in the reaction is given by
moles\ of\ AgCl(s)\ formed = moles\ of\ AgNO_{3}(aq)\ or\ NaCl(aq)= (0.500\ L)(0.200\ mol·L^{–1}) = 0.100\ molThe value of ΔH for the formation of 0.100 moles of AgCl(s) is
\Delta H = –c_{P,cal}\Delta T = –(4.60 × 10^{3}\ J·K^{–1})(1.423\ K) = –6550\ Jhis is the value of ΔH for the formation of 0.100 moles; thus, we have
ΔH^{\circ}_{rxn}=\frac{–6550\ J}{0.100\ mol} = –65.5 × 10^{3}\ J·mol^{–1} = –65.5\ kJ·mol^{–1}for the value of ΔH^{\circ}_{rxn} for the formation of one mole of AgCl(s).