How much heat is needed to convert 10g ice to 10g water vapor?

mass * ( heat of fusion + heat capacity * 100 + heat of vaporization)

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To calculate the heat needed to convert ice to water vapor, we need to consider the three different phases and the corresponding heat changes involved.

1. Heating the ice from its initial temperature to its melting point:
The heat required can be calculated using the equation Q = m * Cp * ΔT, where:
- Q represents the heat needed
- m is the mass (10g in this case)
- Cp is the specific heat capacity of ice
- ΔT is the change in temperature, which is the final temperature minus the initial temperature

The specific heat capacity of ice is approximately 2.09 J/g·°C. Assuming the initial temperature of the ice is at -10°C and the melting point of ice is 0°C, the ΔT is 0 - (-10) = 10°C.

Q = 10g * 2.09 J/g·°C * 10°C = 209 J

2. Melting the ice at its melting point:
To convert ice at 0°C to water at 0°C, we need to provide heat for the phase change, known as the heat of fusion. The heat of fusion for ice is approximately 334 J/g.

Q = m * ΔHfus
Q = 10g * 334 J/g = 3340 J

3. Heating the water from its melting point to its boiling point:
The heat required can be calculated using the same equation as in step 1.

The specific heat capacity of water is approximately 4.18 J/g·°C. Assuming the boiling point of water is 100°C, the ΔT is 100 - 0 = 100°C.

Q = 10g * 4.18 J/g·°C * 100°C = 4180 J

4. Vaporizing the water at its boiling point:
To convert water at 100°C to water vapor at 100°C, we need to provide heat for the phase change, known as the heat of vaporization. The heat of vaporization for water is approximately 2260 J/g.

Q = m * ΔHvap
Q = 10g * 2260 J/g = 22600 J

Now, let's sum up the heat changes:

Total heat = Q1 + Q2 + Q3 + Q4
Total heat = 209 J + 3340 J + 4180 J + 22600 J
Total heat = 30129 J

Therefore, approximately 30129 J of heat is needed to convert 10g of ice into 10g of water vapor.

To determine the amount of heat required to convert ice to water vapor, we need to consider two phase changes: the melting of ice into liquid water and the vaporization of liquid water into water vapor.

First, we calculate the heat required for the ice to melt into water. This can be done using the formula:

Q = m * ΔHf

Where:
- Q is the heat required
- m is the mass of the ice
- ΔHf is the heat of fusion (or latent heat of fusion) for water, which is 334 J/g

Given that the mass (m) of the ice is 10g, we can calculate the heat required for the melting phase change:

Q1 = 10g * 334 J/g = 3340 J

Next, we calculate the heat required for the liquid water to vaporize into water vapor. This can be done using the formula:

Q = m * ΔHv

Where:
- Q is the heat required
- m is the mass of the liquid water
- ΔHv is the heat of vaporization (or latent heat of vaporization) for water, which is 2260 J/g

Since the mass of the liquid water that resulted from the ice is still 10g, we can calculate the heat required for the vaporization phase change:

Q2 = 10g * 2260 J/g = 22600 J

Finally, to calculate the total heat required to convert 10g of ice to 10g of water vapor, we add the heat required for both phase changes:

Total heat = Q1 + Q2 = 3340 J + 22600 J = 25940 J

Therefore, 25,940 J of heat is needed to convert 10g of ice to 10g of water vapor.