How much energy (in kilojoules) is released when 12.3g of steam at 121.5degree C is condensed to give liquid water at 64.5 degree C? The heat of vaporization of liquid water is 40.67 kj/mol, and the molar heat capacity is 75.3 J/(K mol) for the liquid and 33.6 J/(K mol) for the vapor
The easiest way to do this is to do it in steps.
q1 = heat to move steam from 121.5 to 100.
q1 = mass x specific heat steam x delta T.
q2 = heat to condense steam at 100 C to liquid water at 100.
q2 = mass x heat vaporization.
q3 = heat to move liquid water at 100 C to liquid water at 64.5 C.
q3 = mass x specific heat water x delta T.
Total heat removed = q1 + q2 + q3.
34.1kJ
To calculate the energy released when steam is condensed, we need to consider the following steps:
1. Calculate the energy required to cool down the steam from 121.5°C to 100°C
2. Calculate the energy released during the phase transition from steam (at 100°C) to liquid water (at 100°C)
3. Calculate the energy released to cool down the liquid water from 100°C to 64.5°C
Step 1: Calculate the energy required to cool down the steam from 121.5°C to 100°C.
The molar heat capacity for the vapor is given as 33.6 J/(K mol). To convert this to kilojoules per gram, we divide it by the molar mass of water, which is 18.015 g/mol.
Heat required (Q1) = mass of steam * molar heat capacity for the vapor * temperature change
= 12.3g * (33.6 J/(K mol) / 18.015 g/mol) * (121.5°C - 100°C)
= 12.3g * 1.86 kJ/gK * 21.5°C
= 536.57 kJ
Step 2: Calculate the energy released during the phase transition.
The heat of vaporization of liquid water is given as 40.67 kJ/mol. We need to convert it to kilojoules per gram.
Heat released (Q2) = mass of steam * heat of vaporization
= 12.3g * (40.67 kJ/mol / 18.015 g/mol)
= 27.72 kJ
Step 3: Calculate the energy released to cool down the liquid water from 100°C to 64.5°C.
The molar heat capacity for the liquid is given as 75.3 J/(K mol).
Heat released (Q3) = mass of liquid water * molar heat capacity for the liquid * temperature change
= 12.3g * (75.3 J/(K mol) / 18.015 g/mol) * (100°C - 64.5°C)
= 12.3g * 4.17 kJ/gK * 35.5°C
= 1824.92 kJ
Total energy released = Q1 + Q2 + Q3
= 536.57 kJ + 27.72 kJ + 1824.92 kJ
= 2389.21 kJ
Therefore, the total energy released when 12.3g of steam at 121.5°C is condensed to liquid water at 64.5°C is 2389.21 kilojoules.
To calculate the energy released during the condensation of steam to liquid water, we need to follow a few steps:
1. Convert the mass of steam to moles: To do this, we use the molar mass of water (18.015 g/mol).
moles of steam = mass of steam / molar mass of water
moles of steam = 12.3 g / 18.015 g/mol
2. Calculate the heat absorbed during cooling the steam and condensing it to liquid water. This involves two parts:
a. Calculate the heat absorbed to lower the temperature from 121.5 °C to 100 °C. We use the molar heat capacity (C) for vapor for this calculation.
q1 = moles of steam × C (vapor) × ΔT
where ΔT is the change in temperature (121.5 °C - 100 °C)
b. Calculate the heat absorbed to condense the steam at 100 °C into liquid water at 100 °C. This is the heat of vaporization (ΔHvap).
q2 = moles of steam × ΔHvap
3. Calculate the heat released during cooling the liquid water from 100 °C to 64.5 °C. This involves using the molar heat capacity (C) for liquid.
q3 = moles of liquid water × C (liquid) × ΔT
where ΔT is the change in temperature (100 °C - 64.5 °C)
4. Finally, add up the three heat values to get the total energy released during condensation:
total energy released = q1 + q2 + q3
Let's plug in the given values and calculate the answer:
moles of steam = 12.3 g / 18.015 g/mol
moles of steam ≈ 0.682 mol
q1 = 0.682 mol × 33.6 J/(K mol) × (121.5 °C - 100 °C)
q1 ≈ 502.84 J
q2 = 0.682 mol × 40.67 kJ/mol
q2 ≈ 27.76 kJ
moles of liquid water = 0.682 mol (since the number of moles remains the same in the condensation process)
q3 = 0.682 mol × 75.3 J/(K mol) × (100 °C - 64.5 °C)
q3 ≈ 1680.18 J
total energy released = q1 + q2 + q3
total energy released ≈ 27.76 kJ + 502.84 J + 1680.18 J
total energy released ≈ 28.27 kJ + 2182.02 J
total energy released ≈ 30.45 kJ
Therefore, approximately 30.45 kilojoules (kJ) of energy is released during the condensation process.