To calculate the total heat flow for the process of melting 36 g of ice at 0 °C and bringing the resulting water to 25 °C, we need to consider two steps:
- The heat required to melt the ice at 0 °C.
- The heat required to raise the temperature of the resulting water from 0 °C to 25 °C.
I. Heat required to melt the ice
The heat required to melt the ice is given by the formula:
\[ q_{\text{fusion}} = n \cdot \Delta H_{\text{fusion}} \]
where:
- \( n \) is the number of moles of ice, and
- \( \Delta H_{\text{fusion}} \) is the heat of fusion.
First, we need to calculate the number of moles of ice. The molar mass of water (H₂O) is approximately 18.015 g/mol. The number of moles of 36 g of ice is calculated as follows:
\[ n = \frac{m}{M} = \frac{36 , \text{g}}{18.015 , \text{g/mol}} \approx 2.00 , \text{mol} \]
Now we can calculate the heat required to melt the ice:
\[ q_{\text{fusion}} = n \cdot \Delta H_{\text{fusion}} = 2.00 , \text{mol} \times 6.02 , \text{kJ/mol} = 12.04 , \text{kJ} \]
II. Heat required to raise the temperature of water
The heat required to change the temperature of the water is calculated using the formula:
\[ q_{\text{heating}} = m \cdot C \cdot \Delta T \]
where:
- \( m \) is the mass of the water (which is still 36 g after melting),
- \( C \) is the specific heat capacity of water (4.184 J/g°C),
- \( \Delta T \) is the change in temperature (25 °C - 0 °C = 25 °C).
Substituting the values:
\[ q_{\text{heating}} = 36 , \text{g} \times 4.184 , \text{J/g°C} \times 25 , \text{°C} = 36 \times 4.184 \times 25 = 3786 , \text{J} \]
Now convert this value from Joules to kilojoules:
\[ q_{\text{heating}} = \frac{3786 , \text{J}}{1000} = 3.786 , \text{kJ} \]
Total Heat Flow
Now we add the heat absorbed for both processes:
\[ q_{\text{total}} = q_{\text{fusion}} + q_{\text{heating}} = 12.04 , \text{kJ} + 3.786 , \text{kJ} = 15.826 , \text{kJ} \]
Thus, the total heat flow for the system during this process is approximately 15.83 kJ.
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