Step-by-step explanation:
The amount of heat required to melt a solid substance is given by the formula:
Q = m * ΔHf
where Q is the amount of heat required, m is the mass of the substance, and ΔHf is the heat of fusion of the substance. The heat of fusion of ethanol is 111.3 J/g.
So, for melting 148 g of solid ethanol, the amount of heat required is:
Q1 = 148 g * 111.3 J/g = 16499.6 J
The amount of heat required to raise the temperature of the liquid ethanol from -26.8°C to its melting point of -114.1°C is given by the formula:
Q2 = m * C * ΔT
where Q2 is the amount of heat required, m is the mass of the substance, C is its specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of ethanol is 2.44 J/g°C. The change in temperature is:
ΔT = (-114.1°C) - (-26.8°C) = -87.3°C
Since we want to bring the ethanol to its melting point, we assume that it is still in the liquid state. Therefore, we use the specific heat capacity of liquid ethanol for this calculation.
So, for raising the temperature of 148 g of liquid ethanol from -26.8°C to -114.1°C, the amount of heat required is:
Q2 = 148 g * 2.44 J/g°C * (-87.3°C) = -30834.8 J
Note that the negative sign indicates that heat is lost from the ethanol as it cools.
The total amount of heat required to melt 148 g of solid ethanol and bring it to a temperature of -26.8°C is the sum of Q1 and Q2:
Qtotal = Q1 + Q2 = 16499.6 J + (-30834.8 J) = -14335.2 J
The answer is -14335 J (rounded to three significant digits), which means that 14335 J of heat energy must be removed from the system (or the surroundings must supply 14335 J of heat energy) to carry out the process as described.