How much energy (in kilojoules) is released when 12.3g of steam at 121.5 degree C is condensed to give liquid water at 64.5 degree C? The heat of vaporization of liquid water is 40.67kj/mol , and the molar heat capacity is 75.3 J/(K mol) for the liquid and 33.6 J/(K mol)for the vapor

Question

How much energy (in kilojoules) is released when 12.3g of steam at 121.5 degree C is condensed to give liquid water at 64.5 degree C? The heat of vaporization of liquid water is 40.67kj/mol , and the molar heat capacity is 75.3 J/(K mol) for the liquid and 33.6 J/(K mol)for the vapor

Answer 1

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Answer 2

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Answer 3

To calculate the energy released when steam is condensed, we need to consider two steps: the energy required to cool the steam from 121.5 degrees Celsius to 100 degrees Celsius and then the energy released when the steam condenses to liquid water at 100 degrees Celsius.

Step 1: Calculate the energy required to cool the steam from 121.5 degrees Celsius to 100 degrees Celsius.
To do this, we'll use the heat capacity formula: ΔQ = m × C × ΔT, where ΔQ is the energy, m is the mass, C is the heat capacity, and ΔT is the change in temperature.

Given:
Mass of steam (m) = 12.3g = 0.0123kg
Heat capacity (C) = 33.6 J/(K mol)
Initial temperature (T1) = 121.5 degrees Celsius
Final temperature (T2) = 100 degrees Celsius

First, convert the temperatures from degrees Celsius to Kelvin:
T1 = 121.5 + 273.15 = 394.65 K
T2 = 100 + 273.15 = 373.15 K

Next, calculate the energy required to cool the steam:
ΔQ1 = 0.0123kg × 33.6 J/(K mol) × (T1 - T2) = 0.0123kg × 33.6 J/(K mol) × (394.65 K - 373.15 K)

Step 2: Calculate the energy released when the steam condenses to liquid water at 100 degrees Celsius.
This energy is equal to the heat of vaporization of liquid water.

Given:
Heat of vaporization (ΔHvap) = 40.67 kJ/mol

Now, convert the moles of water to determine the energy released:
molar mass of water (H2O) = 18.015 g/mol
moles of water = mass (g) / molar mass (g/mol)
moles of water = 12.3 g / 18.015 g/mol

Finally, calculate the energy released:
ΔQ2 = moles of water × ΔHvap

To find the total energy released, add the two steps together:
Total energy released = ΔQ1 + ΔQ2

Make sure to perform the conversions and calculations to get the final value in kilojoules (kJ).