Answer:
To calculate the amount of heat needed to melt 108 g of solid hexane and bring it to a temperature of -56.0 Celsius, we need to use the specific heat of hexane and the heat of fusion of hexane. The specific heat of hexane is 1.76 J/g*K, and the heat of fusion of hexane is 3.00 kJ/mol
- First, we need to calculate the amount of heat needed to melt the solid hexane. This can be calculated using the formula Q = m * ΔHfus, where Q is the amount of heat, m is the mass of hexane, and ΔHfus is the heat of fusion of hexane. The mass of hexane is 108 g, and the heat of fusion of hexane is 3.00 kJ/mol. The molar mass of hexane is 86.18 g/mol.
Q1 = 108 g * (1 mol / 86.18 g) * 3.00 kJ/mol = 3.33 kJ
- Next, we need to calculate the amount of heat needed to bring the melted hexane to a temperature of -56.0 Celsius. This can be calculated using the formula Q = m * C * ΔT, where Q is the amount of heat, m is the mass of hexane, C is the specific heat of hexane, and ΔT is the change in temperature. The mass of hexane is still 108 g, the specific heat of hexane is 1.76 J/g*K, and the change in temperature is (273.15 K - 56.0 K) = 217.15 K.
Q2 = 108 g * 1.76 J/g*K * 217.15 K = 41.3 kJ
- The total amount of heat needed to melt 108 g of solid hexane and bring it to a temperature of -56.0 Celsius is the sum of Q1 and Q2:
Qtotal = Q1 + Q2 = 3.33 kJ + 41.3 kJ = 44.6 kJ
- Therefore, the amount of heat needed to melt 108 g of solid hexane and bring it to a temperature of -56.0 Celsius is 44.6 kJ. The unit symbol is kJ, and the answer has three significant digits.