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 calculate the amount of heat required to warm the ice to steam, we need to consider the following steps:
Step 1: Calculate the heat required to raise the temperature of the ice from -15.0∘C to 0∘C (melting point of ice).
Step 2: Calculate the heat required to melt the ice at 0∘C.
Step 3: Calculate the heat required to raise the temperature of the water from 0∘C to 100∘C (boiling point of water).
Step 4: Calculate the heat required to vaporize the water at 100∘C.
Step 5: Calculate the heat required to raise the temperature of the steam from 100∘C to 114∘C.
Let's go through each step:
Step 1: Calculate the heat required to raise the temperature of the ice from -15.0∘C to 0∘C.
Heat = mass × specific heat × temperature change
Heat = 10.0 g × 2.09 J/g⋅∘C × (0 - (-15.0))
Heat = 10.0 g × 2.09 J/g⋅∘C × 15.0∘C
Heat = 313.5 J
Step 2: Calculate the heat required to melt the ice at 0∘C.
Heat = mass × heat of fusion
Heat = 10.0 g × 334 J/g (heat of fusion of ice)
Heat = 3340 J
Step 3: Calculate the heat required to raise the temperature of water from 0∘C to 100∘C.
Heat = mass × specific heat × temperature change
Heat = 10.0 g × 4.18 J/g⋅∘C × (100 - 0)
Heat = 4180 J
Step 4: Calculate the heat required to vaporize the water at 100∘C.
Heat = mass × heat of vaporization
Heat = 10.0 g × 2260 J/g (heat of vaporization of water)
Heat = 22600 J
Step 5: Calculate the heat required to raise the temperature of steam from 100∘C to 114∘C.
Heat = mass × specific heat × temperature change
Heat = 10.0 g × 2.01 J/g⋅∘C × (114 - 100)
Heat = 282 J
Now, we can sum up the heat from each step to find the total heat required:
Total heat = 313.5 J + 3340 J + 4180 J + 22600 J + 282 J
Total heat = 30315.5 J
To convert the heat to kilojoules (kJ):
Total heat = 30315.5 J ÷ 1000
Total heat ≈ 30.3 kJ
Therefore, approximately 30.3 kJ of heat is required to warm 10.0 g of ice, initially at -15.0∘C, to steam at 114.0∘C.