How much heat (in kJ) is required to warm 13.0 g of ice, initially at -13.0 ∘C, to steam at 111.0 ∘C? The heat capacity of ice is 2.09 J/g⋅∘C and that of steam is 2.01 J/g⋅∘C.
I'm just an ordinary student like you so I might be wrong but it's
H2O x Specific heat(2.09 J/g⋅C) x delta T
x stands for multiplication and delta T is change in temperature
To calculate the amount of heat required to warm the ice to steam, we need to consider the heat required at different stages:
1. Heating the ice from -13.0 ∘C to 0 ∘C:
- We can use the specific heat capacity of ice to calculate the heat required in this step.
- The formula to calculate the heat required is: q = mass × specific heat capacity × temperature change.
- The mass of ice is 13.0 g, the specific heat capacity is 2.09 J/g⋅∘C, and the temperature change is 0 ∘C - (-13.0 ∘C) = 13.0 ∘C.
- Plugging in the values, we get: q1 = 13.0 g × 2.09 J/g⋅∘C × 13.0 ∘C.
2. Melting the ice to water at 0 ∘C:
- To calculate the heat required for this step, we need to use the heat of fusion for ice.
- The formula to calculate the heat required is: q = mass × heat of fusion.
- The mass of ice is 13.0 g, and the heat of fusion for ice is given by q2 = mass × heat of fusion.
3. Heating the water from 0 ∘C to 100 ∘C:
- We can use the specific heat capacity of water to calculate the heat required in this step.
- The formula to calculate the heat required is: q = mass × specific heat capacity × temperature change.
- Since water's specific heat capacity is assumed to be the same as ice, which is 2.09 J/g⋅∘C, we can use the same formula as step 1.
- The mass of water is the same as the mass of ice, 13.0 g, and the temperature change is 100 ∘C - 0 ∘C = 100 ∘C.
- Plugging in the values, we get: q3 = 13.0 g × 2.09 J/g⋅∘C × 100 ∘C.
4. Vaporizing the water to steam at 100 ∘C:
- To calculate the heat required for this step, we need to use the heat of vaporization for water.
- The formula to calculate the heat required is: q = mass × heat of vaporization.
- The mass of water is 13.0 g, and the heat of vaporization for water is given by q4 = mass × heat of vaporization.
5. Heating the steam from 100 ∘C to 111 ∘C:
- We can use the specific heat capacity of steam to calculate the heat required in this step.
- The formula to calculate the heat required is: q = mass × specific heat capacity × temperature change.
- The mass of steam is also 13.0 g, and the specific heat capacity is 2.01 J/g⋅∘C.
- The temperature change is 111 ∘C - 100 ∘C = 11 ∘C.
- Plugging in the values, we get: q5 = 13.0 g × 2.01 J/g⋅∘C × 11 ∘C.
Finally, to find the total heat required to warm the ice to steam, we add up all the individual heat quantities:
Total heat = q1 + q2 + q3 + q4 + q5
Simply substitute the given values into the equations to calculate the total heat.