Question

How much heat is evolved in converting 1.00 mol of steam at 160.0 ∘C to ice at -50.0 ∘C? The heat capacity of steam is 2.01 J/(g⋅∘C) and of ice is 2.09 J/(g⋅∘C).

Answer 1

There are multiple stages involved in the process of cooling the steam to ice .

Let's calculate heat evolved at each step separately.

Q1 = Amount of heat evolved in cooling the steam from 160 degree C to 100 degree C.

Q1 = m * C_steam * Delta T

Here, m is mass of steam. 1 mol steam is equal to molar mass of water which is 18.02 g , so m = 18.02 g

C_steam is the heat capacity of steam which is given as 2.01 J/(g⋅∘C)

Delta T is the difference in temperature, which is 100.0 C - 160.0 C = - 60.0 C

Q1 = 18.02 g * 2.01 J/(g⋅∘C) * (-60.0 C )

Q1 = -2173 J = -2.17 kJ

Q2 = Heat of condensation of steam

At this stage, all the steam which is at 100 C will get converted to liquid water at 100 C. The temperature will remain constant during this change as it is a phase change.

Heat of condensation is constant for a given substance and it is equal to heat of vaporization but has negative sign which indicates that heat is evolved.

For water, heat of vaporization is 40.65 kJ / mol

Therefore, Q2 = - 40.65 kJ / mol

Q3 = Amount of heat evolved in changing temperature of water from 100 C to 0 C

Q3 = m * C_water * Delta T

C_water is specific heat of water which is 4.184 J/g C

Delta T = 0 C - 100 C = -100 C

Q3 = 18.02 g * 4.184 J/ g C * (-100 C )

Q3 = -7540 J = -7.54 kJ

Q4 = Heat evolved in converting water at 0 C to solid ice at 0 C. This is again a phase change and therefore temperature will remain constant.

Enthalpy of fusion is a constant and for water it is 6.01 kJ/ mol

Therefore Q4 = - 6.01 kJ/mol

Q5 = Heat evolved in changing temperature of ice from 0 C to -50 C

Q5 = m * C_ice * delta T

C_ice is heat capacity of ice and it is given as 2.09 J/(g⋅∘C)

Delta T is -50 C - 0 C = - 50 C

Q5 = 18.02 g * 2.09 J/(g⋅∘C) * (-50 C )

Q5 = -1883 J = - 1.88 kJ

Total heat evolved during the process is

Q = Q1 + Q2 + Q3 + Q4 + Q5

Q = -2.17 kJ + ( - 40.65 kJ ) + ( -7.54 kJ ) + ( - 6.01 kJ) + ( - 1.88 kJ)

Q = -58.3 kJ

Total heat evolved during the process is 58.3 kJ

( Note : Negative sign indicates that heat is evolved)