A 15.0-g sample of ice at -15.0 °C is heated until it becomes liquid water at 45.0 °C. How much energy (in joules) is required for this process? (Given: specific heat of ice = 2.09 J/g·°C, specific heat of water = 4.18 J/g·°C, heat of fusion of ice = 334 J/g)

• A. 9,120 J
• B. 3,980 J
• C. 7,740 J
• D. 5,320 J

Answer: (C)

Verified step by step guidance

1. First, calculate the energy required to raise the temperature of the ice from -15.0 °C to 0 °C using the specific heat capacity of ice. Use the formula: \(q_1 = m \times C_{ice} \times \Delta T\), where \(m\) is the mass, \(C_{ice}\) is the specific heat of ice, and \(\Delta T\) is the temperature change.
2. Next, calculate the energy required to melt the ice at 0 °C into liquid water at 0 °C using the heat of fusion. Use the formula: \(q_2 = m \times \Delta H_{fusion}\), where \(\Delta H_{fusion}\) is the heat of fusion of ice.
3. Then, calculate the energy required to raise the temperature of the resulting liquid water from 0 °C to 45.0 °C using the specific heat capacity of water. Use the formula: \(q_3 = m \times C_{water} \times \Delta T\), where \(C_{water}\) is the specific heat of water.
4. Add all the energy values together to find the total energy required: \(q_{total} = q_1 + q_2 + q_3\).
5. Make sure to keep track of units throughout the calculations and express the final answer in joules.