Calculate the amount of heat needed to melt 53.7g of solid acetic acid (HCH3CO2) and bring it to a temperature of 111.2°C. Be sure your answer has a unit symbol and the correct number of significant digits.

To solve this problem, we need to know the specific heat, melting point, and heat of fusion of acetic acid. The specific heat of acetic acid is 2.09 J/g°C, its melting point is 16.6°C, and its heat of fusion is 11.3 kJ/mol.

First, we need to calculate the amount of heat needed to raise the temperature of the solid acetic acid from its melting point to 0°C.

q1 = mass * specific heat * change in temperature q1 = 53.7g * 2.09 J/g°C * (16.6°C - 0°C) = 1836.7 J

Next, we need to calculate the amount of heat needed to melt the acetic acid.

First, convert the mass of acetic acid to moles. The molar mass of acetic acid is 60.052 g/mol.

moles = 53.7g / 60.052 g/mol = 0.894 mol

Then, calculate the heat of fusion.

q2 = moles * heat of fusion q2 = 0.894 mol * 11.3 kJ/mol = 10.1 kJ = 10100 J

Finally, we need to calculate the amount of heat needed to raise the temperature of the liquid acetic acid from its melting point to 111.2°C.

q3 = mass * specific heat * change in temperature q3 = 53.7g * 2.09 J/g°C * (111.2°C - 16.6°C) = 10596.7 J

The total amount of heat needed is the sum of q1, q2, and q3.

q_total = q1 + q2 + q3 = 1836.7 J + 10100 J + 10596.7 J = 22533.4 J

So, the amount of heat needed to melt 53.7g of solid acetic acid and bring it to a temperature of 111.2°C is approximately 22533 J.