An ice calorimeter, shown below, can be used to measure the amount of heat released or absorbed by a reaction that is carried out at a constant temperature of $0 .{ }^{\circ} \mathrm{C}$. If heat is transferred from the system to the bath, some of the ice melts. A given mass of liquid water has a smaller volume than the same mass of ice, so the total volume of the ice and water mixture decreases. Measuring the volume decrease using the scale at the left indicates the amount of heat released by the reacting system. As long as some ice remains in the bath, the temperature remains at $0 .{ }^{\circ} \mathrm{C}$. In Example $15-2$ we saw that the reaction
$\mathrm{CuSO}_{4}(\mathrm{aq})+2 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow \mathrm{Cu}(\mathrm{OH})_{2}(\mathrm{~s})+\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})$
releases $846 \mathrm{~J}$ of heat at constant temperature and pressure when $50.0 \mathrm{~mL}$ of $0.400 \mathrm{M} \mathrm{CuSO}_{4}$ solution and $50.0 \mathrm{~mL}$
of $0.600 \mathrm{M} \mathrm{NaOH}$ solution are allowed to react. (Because no gases are involved in the reaction, the volume change of the reaction mixture is negligible.) Calculate the change in volume of the ice and water mixture that would be observed if we carried out the same experiment in an ice calorimeter. The density of $\mathrm{H}_{2} \mathrm{O}(\ell)$ at $0 .{ }^{\circ} \mathrm{C}$ is $0.99987$ $\mathrm{g} / \mathrm{mL}$ and that of ice is $0.917 \mathrm{~g} / \mathrm{mL} .$ The heat of fusion of ice at $0^{\circ} \mathrm{C}$ is $334 \mathrm{~J} / \mathrm{g}$.