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Answer :
The enthalpy of fusion of sodium acetate is [tex]\( 150.48 \ \text{J/g} \).[/tex]
1. Calculate the heat gained by the water:
The formula for heat transfer is:
[tex]\[ q = m \cdot c \cdot \Delta T \][/tex]
Given:
- [tex]\( m_{\text{water}} = 500 \ \text{g} \)[/tex]
- [tex]\( c_{\text{water}} = 4.18 \ \text{J/g}^\circ \text{C} \)[/tex]
- [tex]\( \Delta T = 39.4^\circ \text{C} - 25.0^\circ \text{C} = 14.4^\circ \text{C} \)[/tex]
Now, calculate the heat absorbed by the water:
[tex]\[ q_{\text{water}} = 500 \ \text{g} \cdot 4.18 \ \text{J/g}^\circ \text{C} \cdot 14.4^\circ \text{C} \][/tex]
[tex]\[ q_{\text{water}} = 500 \cdot 4.18 \cdot 14.4 \][/tex]
[tex]\[ q_{\text{water}} = 30,096 \ \text{J} \][/tex]
2. Calculate the enthalpy of fusion of sodium acetate:
The heat absorbed by the water is equal to the heat released by the sodium acetate during crystallization. This heat can be used to find the enthalpy of fusion per gram of sodium acetate.
Given:[tex]\[ q_{\text{water}} = 30,096 \ \text{J} \][/tex]
- Mass of sodium acetate = 200 g
- Heat released by sodium acetate = Heat absorbed by water = [tex]\( 30,096 \ \text{J} \)[/tex]
The enthalpy of fusion [tex](\( \Delta H_f \))[/tex] per gram of sodium acetate is:
[tex]\[ \Delta H_f = \frac{q_{\text{water}}}{m_{\text{sodium\ acetate}}} \][/tex]
[tex]\[ \Delta H_f = \frac{30,096 \ \text{J}}{200 \ \text{g}} \][/tex]
[tex]\[ \Delta H_f = 150.48 \ \text{J/g} \][/tex]
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