Question

When a student mixed $50mL$ of $1.0M$ $HCl$ and $50mL$ of $1.0M$ $NaOH$ in a coffee cup calorimeter, the temperature of the resultant solution increases from ${21}^{o}C$ to ${27.5}^{o}C$. Assuming that the calorimeter absorbs only a negligible quantity of heat, that the total volume of solution is $100mL$, its density $1.0g$ ${mL}^{-1}$ and that its specific heat is $4.18J/g$. Calculate:
(a) the heat change during mixing.
(b) the enthalpy change for the reaction:
$HC{l}_{(aq.)}+NaO{H}_{(aq.)}\to NaC{l}_{(aq.)}+H_{2}O$

Answer 1

(a) Number of moles of $HCl$ and $NaOH$ added
$=\frac{MV}{1000}=\frac{1\times 50}{1000}=0.05$
Mass of mixture $=V\times d=100\times =100g$
Heat evolved, $q=ms\Delta T=100\times 4.18\times (27.5-21.0)$
$=100\times 4.18\times 6.5J=2717J=2.717kJ$

(b) The involved reaction is:
$HCl(aq.)+NaOH(aq.)\to NaCl(aq.)+H_{2}O$
$\Delta H=$ Heat evolved per mol
$=\frac{-2.717}{0.05}=-54.34kJ$