Question

How much heat is evolved in converting 1.00 mol of steam at 150.0 ∘C to ice at -45.0 ∘C? The heat capacity of steam is 2.01 J/(g⋅∘C) and of ice is 2.09 J/(g⋅∘C).

Answer 1

Total Heat from Ice to Vapor

We require 2 type of heat, latent heat and sensible heat

Sensible heat (CP): heat change due to Temperature difference

Latent heat (LH): Heat involved in changing phases (no change of T)

Then

Q1 = m*Cp ice * (Tf – T1)

Q2 = m*LH ice

Q3 = m*Cp wáter * (Tb – Tf)

Q4 = m*LH vap

Q5 = m*Cp vap* (T2 – Tb)

Note that Tf = 0°C; Tb = 100°C, LH ice = 334 kJ/kg; LH water = 2264.76 kJ/kg.

Cp ice = 2.01 J/g°C ; Cp water = 4.184 J/g°C; Cp vapor = 2.030 kJ/kg°C

Then

Q1 = m*2.01 * (0 – T1)

Q2 = m*334

Q3 = m*4.184 * (100 – 0)

Q4 = m*2264.76

Q5 = m*2.03* (T2 – 100)

QT = Q1+Q2+Q3+Q4+Q5 = m*(2.01 * (0 – T1) + 334 + 4.184 * (100 – 0) + 2264.76 + 2.03* (T2 – 100) )

substitute temperatures

1 mol of water = 18 g of water

QT =  18*(2.01 * (0 – -45) + 334 + 4.184 * (100 – 0) + 2264.76 + 2.03* (150– 100) )

QT = 57763.98 J

QT = 57.76 kJ will be evolved

Answer 2

Answer – We are given, moles of steam = 1.00 mol , ti = 150.0^oC , tf = -45.0^oC

The heat capacity of steam = 2.01 J/g⋅∘C , ice = 2.09 J/g⋅∘C

Mass of steam = 1.00 mole * 18.015 g/mol

                        = 18.015 g

Now first we need to calculate the heat from he 150^oC to 100^oC

q1 = m * C * ∆t

     = 18.015 g * 2.01 J/g⋅^∘C * (100^oC - 150^oC)

     = -1810.5 J

Heat from the 100^oC to 100^oC

q2 = m * ∆Hvap

      = 18.015 g * 2260 J/g

      = - 40713.9 J

Heat from the 100^oC to 0.0^oC

q3 = m * C * ∆t

      = 18.015 g * 4.184 J/g⋅^∘C * (0.0^oC - 100^oC)

      = - 7537.5 J

Heat from the 0.0^oC to 0.0^oC

q4 = m * ∆Hfus

      = 18.015 g * 334 J/g

      = - 6017.01 J

Heat from the 0.0^oC to -45.0^oC

q5 = m * C * ∆t

      = 18.015 g * 2.09 J/g⋅^∘C * (-45.0^oC – 0.0^oC)

      = - 1694.3 J

So total heat

q = q1 + q2 +q3 +q4 +q5

   = -1810.5 -40713.9-7537.5-6017.01-1694.3

   = -5777.2 J

   = -57.8 kJ

So, -57.8 kJ heat is evolved in converting 1.00 mol of steam at 150.0 ∘C to ice at -45.0 ∘C?