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Multiple Choice
Given 307.5 g of hot tea at 73.5 °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
45.2 g
B
62.8 g
C
95.3 g
D
78.5 g
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Verified step by step guidance
1
Identify the heat lost by the hot tea as it cools from 73.5 °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.
Calculate the change in temperature for the tea: \( \Delta T = 12.5 \text{ °C} - 73.5 \text{ °C} \).
Calculate the heat lost by the tea using the specific heat capacity \( c = 4.18 \text{ J/(g·°C)} \) and the mass of the tea \( m = 307.5 \text{ g} \).
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 \( \Delta H_{\text{fusion}} = 6.01 \text{ kJ/mol} \). Convert this energy to joules.
Set the heat lost by the tea equal to the heat gained by the ice (both melting and warming to 12.5 °C) and solve for the mass of ice. Remember to convert the mass of ice to moles using the molar mass of water (18.02 g/mol) and account for both the melting and warming processes.