Calculate the amount of heat needed to melt 46.0g of solid benzene (C6H6) and bring it to a temperature of 13.7°C. Be sure your answer has a unit symbol and the correct number of significant digits.
Question
Calculate the amount of heat needed to melt 46.0g of solid benzene (C6H6) and bring it to a temperature of 13.7°C. Be sure your answer has a unit symbol and the correct number of significant digits.
Solution
To solve this problem, we need to know the specific heat, melting point, and heat of fusion of benzene. The specific heat of benzene is 1.996 J/g°C, the melting point is 5.5°C, and the heat of fusion is 9.95 kJ/mol.
First, we need to calculate the amount of heat needed to raise the temperature of benzene from 5.5°C to 13.7°C.
q = mcΔT
where: m = mass = 46.0 g c = specific heat = 1.996 J/g°C ΔT = change in temperature = 13.7°C - 5.5°C = 8.2°C
q = 46.0 g * 1.996 J/g°C * 8.2°C = 754.472 J
Next, we need to calculate the amount of heat needed to melt benzene.
q = nΔHf
where: n = number of moles = mass/molar mass = 46.0 g / 78.11 g/mol = 0.589 mol ΔHf = heat of fusion = 9.95 kJ/mol = 9950 J/mol
q = 0.589 mol * 9950 J/mol = 5860.55 J
Finally, we add the two amounts of heat together to get the total heat needed.
q_total = q1 + q2 = 754.472 J + 5860.55 J = 6614.922 J
So, the amount of heat needed to melt 46.0g of solid benzene and bring it to a temperature of 13.7°C is approximately 6615 J.
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