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) Q₁ = 58.82 KJ

b) Q₂ = 42.48 KJ

c) Q₃ = 29.22 KJ

d) Q = 130.52 KJ  

Explanation:

a)

In order to find the energy absorbed to heat the solid, we will use:

where,

Q₁ = Heat absorbed for heating solid = ?

m = mass of solid = 488.3 g = 0.4883 kg

C₁ = Specific Heat Capacity of Solid = 2.96 J/g °C

ΔT₁ =  Change in temperature of Solid = Melting Temperature - Initial Temp.

ΔT₁ = 17.6°C - (-23.1°C) = 40.7°C

Therefore,

Q₁ = 58.82 KJ

b)

In order to find the absorbed to melt the solid at 17.6°C, we will use:

where,

Q₂ = Heat absorbed for melting solid = ?

H_fus = Heat of Fusion = 8.04 KJ/mol

n = no. of moles =

Therefore,

Q₂ = 42.48 KJ

c)

In order to find the energy absorbed to heat the liquid, we will use:

where,

Q₃ = Heat absorbed for heating Liquid = ?

m = mass of solid = 488.3 g = 0.4883 kg

C₃ = Specific Heat Capacity of Liquid = 1.75 J/g °C

ΔT₃ =  Change in temperature of Liquid = Final Temp. - Melting Temp.

ΔT₃ = 51.8°C - 17.6°C = 34.2°C

Therefore,

Q₃ = 29.22 KJ

d)

Total amount of energy absorbed during entire process is:

Q = 130.52 KJ

a:

by the combination of an unlimited number of elements