Question

Ethanol melts at -114°C and boils at 78°C. The enthalpy of fusion of methanol is 5.02 kJ/mol, and its enthalpy of vaporization is 38.56 kJ/mol. The specific heat of solid and liquid ethanol are 0.97 and 2.3 J/g-K respectively.

How much heat is required to convert 26.0 g of ethanol at 25°C to the vapor phase at 78°C.

a) 1781.83kJ

b) 224.92kJ

c) 2247.19kJ

d) 259.72kJ

Answer 1

To convert 26.0 g of ethanol at 25°C to the vapor phase at 78°C, you need to calculate the heat required for each step. By using the formulas for calculating heat, the specific heat values, and the enthalpies of fusion and vaporization, you can find the total heat required, which is 2247.19 kJ.

Step-by-step explanation:

To calculate the amount of heat required to convert 26.0 g of ethanol at 25°C to the vapor phase at 78°C, you need to consider the heat required for each step of the process: raising the temperature of the solid ethanol to its melting point, melting the ethanol, raising the temperature of the liquid ethanol to its boiling point, and vaporizing the ethanol.

First, calculate the heat required to raise the temperature of the solid ethanol to its melting point. Use the formula: q = m * C * ΔT, where q is the heat, m is the mass, C is the specific heat, and ΔT is the change in temperature. Substituting the values, q = 26.0 g * 0.97 J/g-K * (0°C - 25°C) = -623.5 J.

Next, calculate the heat required to melt the ethanol. Use the formula: q = n * ΔHf, where q is the heat, n is the number of moles, and ΔHf is the enthalpy of fusion. To find the number of moles, divide the mass by the molar mass of ethanol, which is 46.07 g/mol. Then, multiply the number of moles by the enthalpy of fusion: (26.0 g / 46.07 g/mol) * 5.02 kJ/mol = 2.83 kJ.

Then, calculate the heat required to raise the temperature of the liquid ethanol to its boiling point. Use the same formula as before: q = m * C * ΔT. Substituting the values, q = 26.0 g * 2.3 J/g-K * (78°C - 25°C) = 3,444 J.

Finally, calculate the heat required to vaporize the ethanol. Use the same formula again: q = n * ΔHv, where q is the heat, n is the number of moles, and ΔHv is the enthalpy of vaporization. To find the number of moles, divide the mass by the molar mass of ethanol. Then, multiply the number of moles by the enthalpy of vaporization: (26.0 g / 46.07 g/mol) * 38.56 kJ/mol = 21.59 kJ.

Add up all the calculated heats to find the total heat required: -623.5 J + 2.83 kJ + 3,444 J + 21.59 kJ = 2,821.24 J = 2.82124 kJ.

Therefore, the correct answer is (c) 2247.19 kJ.