To calculate the heat evolved in converting steam to ice, we need to consider the specific heat capacity and phase changes of water. Here are the steps to find the answer:
1. Determine the specific heat capacity of steam:
The specific heat capacity of steam at constant pressure is approximately 2.03 J/(g*C°).
2. Convert the temperature of steam from Celsius to Kelvin:
Given that the temperature of steam is 145°C, you need to add 273.15 to convert it to Kelvin. So, the temperature becomes 418.15 K.
3. Calculate the heat required to cool the steam to 0°C:
The heat transfer equation is given by:
Heat (q) = mass (m) * specific heat (c) * change in temperature (ΔT)
Since we have 1.00 mol of steam, we need to convert mols to grams by using the molar mass of water.
The molar mass of water (H2O) is approximately 18.015 g/mol.
So, 1.00 mol of water is equal to 18.015 g.
ΔT = 418.15 K - 273.15 K = 145 K
Now, substituting the values into the equation:
q1 = (18.015 g) * (2.03 J/(g°C)) * 145 K
4. Calculate the heat required for the phase change from water to ice at 0°C:
The enthalpy of fusion of water is approximately 6.01 kJ/mol.
To convert this to joules, we multiply by 1000:
Enthalpy of fusion (ΔH) = 6.01 kJ/mol * 1000 = 6010 J/mol
Since we have 1.00 mole of water, we multiply this by ΔH:
q2 = 6010 J/mol
5. Calculate the heat required to cool the ice to -50°C:
The specific heat capacity of ice at constant pressure is approximately 2.09 J/(g°C).
We have already determined that converting 1.00 mole of water to ice requires 18.015 g of water.
ΔT = 273.15 K - (-50°C + 273.15) K = 323.15 K
q3 = (18.015 g) * (2.09 J/(g°C)) * 323.15 K
6. Add up all the values obtained in steps 3, 4, and 5 to find the total heat evolved:
Total heat evolved = q1 + q2 + q3
Make sure to convert all the values to kilojoules (kJ) if necessary.