given the following info for water molar heat of vaporization 40.6kj/mol calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
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To calculate the quantity of heat evolved when 10.0g of steam is condensed, cooled, and frozen to ice at -50 degrees, we need to break down the process into three steps:
1. Condensing steam to water:
The molar heat of vaporization is given as 40.6 kJ/mol. To calculate the heat evolved in condensing the steam, we need to calculate the number of moles of water vapor first.
The molar mass of water (H₂O) is 18.015 g/mol. Using this, we can calculate the number of moles of water vapor:
moles of water vapor = (mass of water vapor) / (molar mass of water)
= (10.0 g) / (18.015 g/mol)
≈ 0.556 mol
Now, we can calculate the heat evolved in condensing the steam using the molar heat of vaporization:
heat evolved = (number of moles of water vapor) * (molar heat of vaporization)
= 0.556 mol * 40.6 kJ/mol
≈ 22.6 kJ
2. Cooling water from 100°C to 0°C:
To calculate the heat evolved in cooling the water, we need to consider the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g°C.
The temperature change is 100°C (from boiling point to 0°C), and the mass of water is 10.0 g. Therefore, the heat evolved in cooling the water can be calculated as:
heat evolved = (mass of water) * (specific heat capacity of water) * (temperature change)
= 10.0 g * 4.18 J/g°C * 100°C
= 4180 J
3. Freezing water to ice at -50°C:
To calculate the heat evolved in freezing water to ice, we need to consider the latent heat of fusion. The latent heat of fusion for water is the same as the molar heat of vaporization, which is 40.6 kJ/mol.
Since the temperature change is -50°C, there is no change in phase at this point. Therefore, the heat evolved can be calculated as zero.
Finally, we sum up the heat evolved in each step:
total heat evolved = heat evolved in condensing steam + heat evolved in cooling water + heat evolved in freezing water
= 22.6 kJ + 4180 J + 0
≈ 22.6 kJ + 4.18 kJ + 0
≈ 26.78 kJ
Therefore, the total quantity of heat evolved when 10.0 g of steam is condensed, cooled, and frozen to ice at -50°C is approximately 26.78 kJ.