How much heat (in kJ) is required to warm 10.0 g of ice, initially at -15.0 ∘C, to steam at 114.0 ∘C? The heat capacity of ice is 2.09 J/g⋅∘C and that of steam is 2.01 J/g⋅∘C.
To determine the amount of heat required to warm the ice to steam, we need to consider the following steps:
1. Heating the ice from -15.0 ∘C to 0 ∘C:
The heat required can be calculated using the formula:
Q = mcΔT, where Q is the heat required, m is the mass, c is the specific heat capacity of ice, and ΔT is the change in temperature.
Q1 = (10.0 g)(2.09 J/g⋅∘C)(0 ∘C - (-15.0 ∘C))
Q1 = (10.0 g)(2.09 J/g⋅∘C)(15.0 ∘C)
2. Melting the ice at 0 ∘C:
The heat required can be calculated using the equation:
Q2 = mL, where Q2 is the heat required, m is the mass, and L is the latent heat of fusion for ice.
Q2 = (10.0 g)(334 J/g)
3. Heating the water from 0 ∘C to 100 ∘C:
Q3 = mcΔT, where Q3 is the heat required, m is the mass, c is the specific heat capacity of water, and ΔT is the change in temperature.
Q3 = (10.0 g)(4.18 J/g⋅∘C)(100 ∘C - 0 ∘C)
4. Boiling the water at 100 ∘C:
Q4 = mL, where Q4 is the heat required, m is the mass, and L is the latent heat of vaporization for water.
Q4 = (10.0 g)(2260 J/g)
5. Heating the steam from 100 ∘C to 114 ∘C:
Q5 = mcΔT, where Q5 is the heat required, m is the mass, c is the specific heat capacity of steam, and ΔT is the change in temperature.
Q5 = (10.0 g)(2.01 J/g⋅∘C)(114 ∘C - 100 ∘C)
Finally, the total heat required is the sum of all the individual heats:
Total heat = Q1 + Q2 + Q3 + Q4 + Q5
Using the given values, we can calculate the result.
To find the heat required to warm a substance through different phases, we need to consider the following steps:
1. Calculate the heat required to raise the temperature from the initial temperature to the melting point (0 °C for ice) while it remains in the solid phase.
2. Calculate the heat required to melt the ice at 0 °C (also known as the heat of fusion).
3. Calculate the heat required to raise the temperature of the water from 0 °C to the boiling point (100 °C for water).
4. Calculate the heat required to vaporize the water at 100 °C (also known as the heat of vaporization).
5. Calculate the heat required to raise the temperature of the steam from the boiling point to the final temperature.
Let's calculate each step:
Step 1: Calculate the heat required to warm the ice from -15.0 °C to 0 °C.
The temperature change is: 0 °C - (-15.0 °C) = 15.0 °C
The heat capacity of ice is 2.09 J/g⋅∘C.
Therefore, the heat required is: 10.0 g × 2.09 J/g⋅∘C × 15.0 °C = 313.5 J
Step 2: Calculate the heat required to melt the ice.
The heat of fusion for ice is usually given as 334 J/g.
Therefore, the heat required is: 10.0 g × 334 J/g = 3340 J
Step 3: Calculate the heat required to warm the water from 0 °C to 100 °C.
The temperature change is: 100 °C - 0 °C = 100 °C
The heat capacity of water is approximately 4.18 J/g⋅∘C.
Therefore, the heat required is: 10.0 g × 4.18 J/g⋅∘C × 100 °C = 4180 J
Step 4: Calculate the heat required to vaporize the water.
The heat of vaporization for water is usually given as 2260 J/g.
Therefore, the heat required is: 10.0 g × 2260 J/g = 22600 J
Step 5: Calculate the heat required to warm the steam from 100 °C to 114.0 °C.
The temperature change is: 114.0 °C - 100 °C = 14.0 °C
The heat capacity of steam is 2.01 J/g⋅∘C.
Therefore, the heat required is: 10.0 g × 2.01 J/g⋅∘C × 14.0 °C = 281.4 J
Finally, add up the heats calculated in each step to find the total heat required:
313.5 J + 3340 J + 4180 J + 22600 J + 281.4 J = 30415.9 J
The heat required to warm 10.0 g of ice from -15.0 °C to steam at 114.0 °C is 30415.9 J (or 30.4 kJ).
warm the ice from -15ºC to 0ºC
melt the ice
warm the water from 0ºC to 100ºC
boil the water
heat the steam to 114ºC
each step has its own heat input