Question

How much heat is evolved in converting 1.00 mol of steam at 135.0 ∘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

To calculate the heat evolved in converting steam at 135.0 °C to ice at -45.0 °C, multiple steps are required, including phase changes and temperature changes within each phase.

Step-by-step explanation:

To determine how much heat is evolved in converting 1.00 mol of steam at 135.0 °C to ice at -45.0 °C, we must account for multiple steps involving specific heat capacities, phase changes, and the enthalpy changes associated with those phase changes. The heat capacity of steam and ice will be used for the temperature changes within those phases, but additional values for the heat of vaporization and fusion for water are required to calculate the energy changes during the phase transitions of steam to liquid water and liquid water to ice.

The calculation involves these main steps:

1. Cooling steam from 135.0 °C to 100 °C (steam at its condensation point)
2. Condensing the steam at 100 °C to liquid water
3. Cooling the water from 100 °C to 0 °C
4. Freezing the water at 0 °C to ice
5. Cooling the ice from 0 °C to -45.0 °C

To complete this calculation, we also need to know the molar mass of water (18.015 g/mol), the enthalpy of vaporization for water (~40.7 kJ/mol), and the enthalpy of fusion for ice (~6.01 kJ/mol).

Once all these values are gathered, we would use the following formulas for each step where q is the heat involved, m is the mass of the substance, C is the specific heat capacity, and ΔT is the change in temperature.

For temperature changes within a single phase: q = m × C × ΔT

For phase changes: q = m × ΔH (where ΔH is the enthalpy change for the phase change)

Answer 2

1 mole of steam (H2O) = 18g
Heat evolved = MCФ where m is the mass and c s specific heat capacity while Ф is change in temperature. Latent heat of fusion is 334 kj/kg while latent heat of vaporization is 2260 kj/kg and specific heat of water is 4.2 j/g/c
= 18 ×2.01 × (135-100) = 1266.3 J
0.018 × 334000 = 6012 J (change of state from gas (steam) to liquid (water)
18 × 4.186× (100 -0) = 7534.8 J
0.018 × 2260000 = 40680 J (change of state from liquid to solid ice)
18 × 2.09 × (0--45) = 1692.9 J
The total heat evolved is therefore 57186 J or 57.186 kJ