How to calculate the amount of heat released when 15.0 g steam at 117°C is converted to ice at -10°C
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How to calculate the amount of heat released when 15.0 g steam at 117°C is converted to ice at -10°C
To calculate the amount of heat released when steam is converted to ice, we need to consider the different phase changes involved and use the specific heat capacities and heat of fusion of water.
Here are the step-by-step calculations:
1. Calculate the heat released during the cooling of steam from 117°C to 100°C.
- The specific heat capacity of steam is 2.03 J/g°C.
- The initial temperature is 117°C, and the final temperature is 100°C.
- Q = m * c * ∆T, where Q is the heat released, m is the mass of steam, c is the specific heat capacity, and ∆T is the change in temperature.
- Q1 = 15.0 g * 2.03 J/g°C * (100°C - 117°C)
2. Calculate the heat released during the phase change from steam at 100°C to water at 100°C.
- The heat of vaporization (or latent heat) of steam is 40.7 kJ/mol.
- The molar mass of water is 18.015 g/mol.
- The heat of vaporization per gram is 40.7 kJ/mol ÷ 18.015 g/mol ≈ 2.26 kJ/g (or 2260 J/g).
- Q2 = 15.0 g * 2.26 kJ/g
3. Calculate the heat released during the cooling of water from 100°C to 0°C.
- The specific heat capacity of water is 4.18 J/g°C.
- The initial temperature is 100°C, and the final temperature is 0°C.
- Q3 = 15.0 g * 4.18 J/g°C * (0°C - 100°C)
4. Calculate the heat released during the phase change from water at 0°C to ice at 0°C.
- The heat of fusion (or latent heat) of water is 333.55 kJ/mol.
- The heat of fusion per gram is 333.55 kJ/mol ÷ 18.015 g/mol ≈ 18.5 kJ/g (or 18500 J/g).
- Q4 = 15.0 g * 18.5 kJ/g
5. Calculate the heat released during the cooling of ice from 0°C to -10°C.
- The specific heat capacity of ice is 2.09 J/g°C.
- The initial temperature is 0°C, and the final temperature is -10°C.
- Q5 = 15.0 g * 2.09 J/g°C * (-10°C - 0°C)
6. Calculate the total heat released by summing up the individual heats released:
- Q_total = Q1 + Q2 + Q3 + Q4 + Q5
Substituting the values and performing the calculations will give you the final answer for the total heat released.
To calculate the amount of heat released when steam is converted to ice, you need to consider the heat gained or lost during each phase change and the temperature change within each phase. We can break down this problem into three steps:
Step 1: Calculate the heat released due to the steam cooling from its initial temperature to the boiling point.
Step 2: Calculate the heat released during the phase change from steam to water at 100°C.
Step 3: Calculate the heat released during the phase change from water to ice at 0°C followed by cooling to -10°C.
Step 1: Calculating the heat released during steam cooling
To calculate the heat released during steam cooling, you need to use the specific heat capacity formula:
Q = m * c * ΔT
Where:
Q = heat energy (in Joules)
m = mass of the substance (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
Given:
Mass of steam (m) = 15.0 g
Specific heat capacity of steam (c) = 2.03 J/g°C (approximate value for steam at atmospheric pressure)
Initial temperature (T1) = 117°C
Final temperature (T2) = 100°C (boiling point)
ΔT = T2 - T1
ΔT = 100°C - 117°C
ΔT = -17°C
Q = 15.0 g * 2.03 J/g°C * -17°C
Step 2: Calculating the heat released during the phase change from steam to water
During the phase change from steam to water at 100°C, the heat released is given by the formula:
Q = m * ΔH
Where:
Q = heat energy (in Joules)
m = mass of the substance (in grams)
ΔH = heat of vaporization (in J/g)
For water at atmospheric pressure, the heat of vaporization is approximately 40.7 kJ/mol (or 40.7 J/g). Therefore:
Q = 15.0 g * 40.7 J/g
Step 3: Calculating the heat released during the phase change from water to ice and cooling to -10°C
During the phase change from water to ice at 0°C, and the subsequent cooling to -10°C, the heat released is given by the formula:
Q = m * ΔH + m * c * ΔT
Where:
Q = heat energy (in Joules)
m = mass of the substance (in grams)
ΔH = heat of fusion (in J/g)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
For water, the heat of fusion is approximately 334 J/g, and the specific heat capacity is approximately 4.18 J/g°C.
Q = 15.0 g * 334 J/g + 15.0 g * 4.18 J/g°C * (-10°C - 0°C)
Once you compute these three steps, you can sum up the values to obtain the total amount of heat released during the entire process.