Question

The energy from condensing water vapor is used to melt ice at 0oC. What mass (kg) of ice can be melted by condensing 0.500 kg of water vapor? (ΔHfus = 6.01 kJ/mol and ΔHvap = 40.7 kJ/mol)

Answer 1

Answer – We are given, mass of water vapor = 0.500 kg , ΔHfus = 6.01 kJ/mol

ΔHvap = 40.7 kJ/mol

First we need to calculate the mass of water vapor kg to g

We know,

1 kg = 1000 g

So, 0.500 kg = ?

= 500 g

Now we need to calculate moles of 500 g of water

Moles of water vapor = 500 g /18.018 g.mol^-1

                                   = 27.75 moles

Nowe we need to calculate the energy released when water gets condensed to liquid from the 500 g of water vapor.

We know the

q = ΔHvap *m

    = 40.7kJ/mol * 27.75 moles

    = 1129.6 kJ

    = 1.3*10⁶ J

So - 1.3*10⁶ J of energy released from the 0.50 kg of water vapor when it gets condensed,

So energy loss = energy gain

So, energy absorbed by ice = 1.3*10⁶ J

So at the melting means fusion of the melt energy formula is

q = ΔHfus * m

so, m = q / ΔHfus

         = 1.3*10⁶ J / 6.01*10³ J/mol

          = 187.95 moles

So, mass of ice = 187.95 moles * 18.015 g/mol

                        = 3386 g of ice

                       = 3.386 kg

So, 3.386 kg of ice can be melted by condensing 0.500 kg of water vapor