How much heat (in kilojoules) is required to warm 11.0 g of ice, initially at -14.0 ∘C, to steam at 112 ∘C? The heat capacity of ice is 2.09 Jg−1∘C−1 and that of steam is 2.01 Jg−1∘C−1.
find the energy (heat) for each step
... the mass of H2O is constant
warm ice to 0ºC
melt ice
warm water to 100ºC
boil water
warm steam to 112ºC
To determine the amount of heat required to warm the ice to steam, we need to calculate the heat required to warm the ice from -14.0 °C to 0 °C, the heat of fusion to melt the ice at 0 °C, the heat required to warm the water from 0 °C to 100 °C, the heat of vaporization to convert the water to steam at 100 °C, and finally, the heat required to warm the steam from 100 °C to 112 °C.
Step 1: Calculate the heat required to warm the ice from -14.0 °C to 0 °C.
Q1 = mass × specific heat capacity × change in temperature
Q1 = 11.0 g × 2.09 Jg^−1∘C^−1 × (0 - (-14.0))
Q1 = 11.0 g × 2.09 Jg^−1∘C^−1 × 14.0 °C
Q1 = 320.68 J
Step 2: Calculate the heat of fusion to melt the ice at 0 °C.
Q2 = mass × heat of fusion
Q2 = 11.0 g × 334 Jg^−1
Q2 = 3674 J
Step 3: Calculate the heat required to warm the water from 0 °C to 100 °C.
Q3 = mass × specific heat capacity × change in temperature
Q3 = 11.0 g × 4.18 Jg^−1∘C^−1 × (100 - 0)
Q3 = 4598.8 J
Step 4: Calculate the heat of vaporization to convert the water to steam at 100 °C.
Q4 = mass × heat of vaporization
Q4 = 11.0 g × 2260 Jg^−1
Q4 = 24860 J
Step 5: Calculate the heat required to warm the steam from 100 °C to 112 °C.
Q5 = mass × specific heat capacity × change in temperature
Q5 = 11.0 g × 2.01 Jg^−1∘C^−1 × (112 - 100)
Q5 = 241.32 J
Now, add up all the calculated heats:
Total heat = Q1 + Q2 + Q3 + Q4 + Q5
Total heat = 320.68 J + 3674 J + 4598.8 J + 24860 J + 241.32 J
Total heat = 33394.8 J
Finally, convert the total heat from joules to kilojoules:
Total heat in kilojoules = Total heat in joules / 1000
Total heat in kilojoules = 33394.8 J / 1000
Total heat in kilojoules ≈ 33.39 kJ
Therefore, the amount of heat required to warm 11.0 g of ice, initially at -14.0 °C, to steam at 112 °C is approximately 33.39 kilojoules.
To solve this problem, we need to calculate the amount of heat necessary to change the temperature of each phase of the substance: ice, water, and steam.
1. First, let's calculate the heat required to warm the ice from -14.0 °C to 0 °C:
- Q1 = mass * specific heat capacity * change in temperature
- Q1 = 11.0 g * 2.09 Jg^(-1)°C^(-1) * (0 °C - (-14.0 °C))
2. Next, we need to calculate the heat required to melt the ice at 0 °C to water at 0 °C:
- Q2 = mass * heat of fusion of ice
- Q2 = 11.0 g * heat of fusion of ice
3. Then, we need to calculate the heat required to warm the water from 0 °C to 100 °C:
- Q3 = mass * specific heat capacity * change in temperature
- Q3 = 11.0 g * 4.18 Jg^(-1)°C^(-1) * (100 °C - 0 °C)
4. After that, we calculate the heat required to vaporize the water at 100 °C to steam at 100 °C:
- Q4 = mass * heat of vaporization of water
- Q4 = 11.0 g * heat of vaporization of water
5. Finally, we need to calculate the heat required to warm the steam from 100 °C to 112 °C:
- Q5 = mass * specific heat capacity * change in temperature
- Q5 = 11.0 g * 2.01 Jg^(-1)°C^(-1) * (112 °C - 100 °C)
The total amount of heat required to go through all these changes is the sum of Q1, Q2, Q3, Q4, and Q5:
Total heat = Q1 + Q2 + Q3 + Q4 + Q5
Now, you can substitute the appropriate values into the equations and calculate the total heat required.