\(\mathrm{CHClF}_{2}\) is a type of hydrochlorofluorocarbon (HCFC) that has a comparatively lower damaging effect on the ozone layer. It is used as a replacement for chlorofluorocarbons (CFCs). The heat of vaporization is \(233.95 \mathrm{~kJ} / \mathrm{g}\). What mass of this substance must evaporate to freeze \(15 \mathrm{~g}\) of water initially at \(15^{\circ} \mathrm{C}\) ? (The heat of fusion of water is \(334 \mathrm{~J} / \mathrm{g} ;\) the specific heat of water is \(4.18 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K} .\) )

To calculate the energy required to cool down the water, we will use the formula: \(Q = mc\Delta T,\) where \(Q\) is the energy required, \(m\) is the mass of the object, \(c\) is the specific heat of the object, and \(\Delta T\) is the change in temperature. In this case, the mass of water is \(15\mathrm{~g}\), the specific heat of water is \(4.18\mathrm{~J/g\cdot K}\), and the change in temperature is from \(15^{\circ}\mathrm{C}\) to \(0^{\circ}\mathrm{C}\), which is a change of \(-15\mathrm{~K}\). So, \(Q_1 = (15\mathrm{~g})(4.18\mathrm{~J/g\cdot K})(-15\mathrm{~K}) = -942.9\mathrm{~J}\). Since we are only interested in the amount of energy required, we will use the absolute value: \(Q_1=942.9\mathrm{~J}\).

To calculate the energy required to freeze the water, we will use the heat of fusion formula: \(Q = mL,\) where \(Q\) is the energy required, \(m\) is the mass of the object, and \(L\) is the heat of fusion of the object. In this case, the mass of water is \(15\mathrm{~g}\), and the heat of fusion of water is \(334\mathrm{~J/g}\). So, \(Q_2 = (15\mathrm{~g})(334\mathrm{~J/g}) = 5010\mathrm{~J}\).

To find the total energy required, we will add the energies found in steps 1 and 2: \(Q_\mathrm{total} = Q_1 + Q_2 = 942.9\mathrm{~J} + 5010\mathrm{~J} = 5952.9\mathrm{~J}\).

To calculate the mass of \(\mathrm{CHClF}_{2}\) needed to provide the required energy by evaporating, we will use the formula: \(m_\mathrm{CHClF_{2}} = \frac{Q_\mathrm{total}}{L_\mathrm{CHClF_{2}}}\), where \(m_\mathrm{CHClF_{2}}\) is the mass of \(\mathrm{CHClF}_{2}\) required, \(Q_\mathrm{total}\) is the total energy required, and \(L_\mathrm{CHClF_{2}}\) is the heat of vaporization of \(\mathrm{CHClF}_{2}\). The heat of vaporization of \(\mathrm{CHClF}_{2}\) is given as \(233.95\mathrm{~kJ/g}\), which is equal to \(233,950\mathrm{~J/g}\). So, \(m_\mathrm{CHClF_{2}} = \frac{5952.9\mathrm{~J}}{233,950\mathrm{~J/g}} = 0.0254\mathrm{~g}\). So, approximately \(0.0254\mathrm{~g}\) of \(\mathrm{CHClF}_{2}\) must evaporate to freeze \(15\mathrm{~g}\) of water initially at \(15^{\circ}\mathrm{C}\).