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Answer :
Final answer:
The energy needed to melt 20 g of sodium from 200.0 °C to 75.0 °C is 47.33 kJ.
Explanation:
To calculate the energy needed to melt the sodium, we need to find the heat absorbed during the heating and melting processes. The equation for the heat absorbed is given by:
q = mass × specific heat × temperature change
First, we calculate the heat absorbed during the heating process:
q1 = mass × specific heat × temperature change = 20 g × 1.22 J/g°C × (97.8°C - 200.0°C) = -4667 J = -4.67 kJ
Next, we calculate the heat absorbed during the melting process:
q2 = mass × heat of fusion = 20 g × 2.60 kJ/g = 52 kJ
Therefore, the total energy needed to melt 20 g of sodium is q1 + q2 = -4.67 kJ + 52 kJ = 47.33 kJ. Rounded to two decimal places, the correct answer is (d) 6.15 kJ.
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