A 488.3 gram sample of an unknown substance (MM = 92.41 g/mol) is heated from -23.1 °C to 51.8 °C. (heat capacity of solid = 2.96 J/g･°C; heat capacity of liquid = 1.75 J/g･°C; ∆Hfus = 8.04 kJ/mol; Tfinal = 17.6 °C) a)How much energy (in kJ) is absorbed/released to heat the solid? b)How much energy (in kJ) is absorbed/released to melt the solid? c)How much energy (in kJ) is absorbed/released to heat the liquid? d)What is the total amount of energy that must be absorbed/released for the entire process?

a) The heat energy absorbed to heat the solid is approximately 58.8 kJ

b) The heat required to melt the solid is approximately 3.93 kJ

c) The heat required to heat the liquid is approximately 29.2 kJ

d) The total amount of energy, absorbed in the entire process is approximately 92 kJ

Explanation:

a) The given parameters are;

The mass of the substance = 488.3 grams

The molar mass of the sample = 92.41g/mol

The temperature change of the substance = -23.1°C to 51.8 °C

The heat capacity of the solid substance = 2.96 J/(g·°C)

The heat capacity of the liquid substance = 1.75 J/(g·°C)

ΔHfus = 8.04 kJ/mol

Taking the melting point temperature of the solid as Tfinal = 17.6 °C, we have;

The heat energy absorbed to heat the solid, Q₁ = 488.3 × 2.96 × (17.6 - (-23.1)) = 58826.4776 J ≈ 58.8 kJ

b) The heat required to melt the solid, Q₂ = ΔHfus × m = 8.04 × 488.3 = 3925.932 J ≈ 3.93 kJ

c) The heat required to heat the liquid, Q₃ = Mass × The specific heat capacity of the liquid × The change in temperature

Therefore;

Q₃ = 488.3 × 1.75 × (51.8 - 17.6) = 29224.755 J ≈ 29.2 kJ

d) The total amount of energy, absorbed in the entire process, ΔQ, is given as follows;

ΔQ = Q₁ + Q₂ + Q₃ = 58826.4776 J + 3925.932 J + 29224.755 J = 91,977.1646 J ≈ 92 kJ