Calculate the total amount of heat (in calories) that would be required to convert 15.0 g of ice at 0 oC to 15.0 g of steam at 100 oC.
q1 = heat to melt ice.
q1 = mass ice x heat fusion.
q2 = heat to raise T of liquid H2O from zero C to 100 C.
q2 = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q3 = heat to vaporize the water
q3 = mass water x heat vaporization.
Total Q = q1 + q2 + q3
9297 calorie
To calculate the total amount of heat required to convert ice at 0°C to steam at 100°C, we need to take into account the different phase changes and the specific heat capacities involved.
The process can be divided into three stages:
1. Heating the ice from 0°C to the melting point of ice.
2. Melting the ice into water at 0°C.
3. Heating the water from 0°C to 100°C and converting it into steam.
Let's calculate each stage separately:
1. Heating the ice to the melting point:
The specific heat capacity of ice is 0.5 cal/g·°C, and the temperature change is from 0°C to melting point (0°C). So the heat required can be calculated as:
Q1 = mass × specific heat capacity × temperature change
Q1 = 15.0 g × 0.5 cal/g·°C × (0 - 0)°C
Q1 = 0 calories
2. Melting the ice into water:
The heat of fusion is the amount of heat required to convert 1 g of ice at 0°C to 1 g of water at 0°C. The heat of fusion of ice is 79.7 cal/g. So the heat required can be calculated as:
Q2 = mass × heat of fusion
Q2 = 15.0 g × 79.7 cal/g
Q2 = 1195.5 calories
3. Heating the water to its boiling point and converting it into steam:
The specific heat capacity of water is 1 cal/g·°C, and the temperature change is from 0°C to boiling point (100°C). So the heat required can be calculated as:
Q3 = mass × specific heat capacity × temperature change
Q3 = 15.0 g × 1 cal/g·°C × (100 - 0)°C
Q3 = 1500 calories
Now, to find the total amount of heat required, we sum up the heat values from each stage:
Total heat = Q1 + Q2 + Q3
Total heat = 0 + 1195.5 + 1500
Total heat = 2695.5 calories
Therefore, the total amount of heat required to convert 15.0 g of ice at 0°C to 15.0 g of steam at 100°C is 2695.5 calories.