Question

A piece of solid antimony weighing 34.3 g at a temperature of 618 °C is placed in 343 g of liquid antimony at a temperature of 754 °C. After a while, the solid melts and a completely liquid sample remains. Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings.

The enthalpy of fusion of solid antimony is ΔH_fus = 19.6 kJ/mol at its melting point of 631 °C, and the molar heat capacities for solid and liquid antimony are C_solid = 25.4 J/mol K and C_liquid = 31.5 J/mol K.

T_final = ______ °C

Answer 1

Let T be the equilibrium temperature

Initial temperature = 754 + 273 = 1027 K

Amount of heat lost by the liquid antimony to reach equilibrium =

Q = 343 x 31.5 x (T - 1027)

Given solid is converted to liquid

Amount of heat required to reach melting point by solid antimony = q₁

Mass of solid antimony = 34.3 g

Initial temperature =T₁= 618 ^oC + 273 = 891 K

Boiling temperature = T₂ = 631 ^oC + 273 = 904 K

Amount of heat required to reach melting point by solid antimony = q₁ = m x c x (T₂-T₁)

Amount heat absorbed by the solid to melt =

Amount of heat absorbed by the liquid to reach equilibrium temperature, T =

The total amount released by liquid = total amount absorbed by solid

Q= q1 + q2+q3

equilibrum temperature or final temperature of both liquids = T = 1014.2 - 273 = 741.2 ^oC