Given 313.5 g of hot tea at 72.5 °C, what mass of ice at 0 °C must be added to obtain iced tea at 12.5 °C? The specific heat of the tea is 4.18 J/(g·°C), and ΔHfusion for ice is +6.01 kJ/mol.

• A. 135.0 g
• B. 45.0 g
• C. 105.0 g
• D. 75.0 g

Answer: (C)

Verified step by step guidance

1. Identify the heat lost by the hot tea as it cools from 72.5 °C to 12.5 °C. Use the formula for heat transfer: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the tea, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
2. Calculate the change in temperature for the tea: \( \Delta T = 72.5 \text{ °C} - 12.5 \text{ °C} \).
3. Calculate the heat lost by the tea using the specific heat capacity: \( q_{\text{tea}} = 313.5 \text{ g} \times 4.18 \text{ J/(g·°C)} \times \Delta T \).
4. Determine the heat required to melt the ice using the formula: \( q = n \cdot \Delta H_{\text{fusion}} \), where \( n \) is the number of moles of ice and \( \Delta H_{\text{fusion}} \) is the enthalpy of fusion. Convert the mass of ice to moles using the molar mass of water (18.02 g/mol).
5. Set the heat lost by the tea equal to the heat gained by the ice to find the mass of ice needed: \( q_{\text{tea}} = q_{\text{ice}} \). Solve for the mass of ice.