In an experiment, 23.0 g of ice at –25°C is converted into steam with a temperature of 124°C. How much heat is required for the process? The following data may be of use:
vap = 2260 J/g; Hfus = 334 J/g; Cp(ice) = 2.06 J/g • °C; Cp(water) = 4.18 J/g • °C;
Cp(steam) = 1.99 J/g • °C
q1 = heat to move ice from -25 C to zero C.
q1 = mass ice x specific heat ice x delta T.
q2 = heat to melt ice (change H2O solid to H2O liquid at zero degrees.)
q2 = mass ice x heat fusion.
q3 = heat to move liquid water from zero degrees C to 100 C.
q3 = mass x specific heat water x delta T.
q4 = heat to convert liquid water at 100 C to steam at 100 C.
q4 = mass x heat vaporization.
q5 = heat to move steam from 100 C to 124 C.
q5 = mass x specific heat steam x delta T.
Total q = q1 + q2 + q3 + q4 + q5.
To calculate the heat required for the process, we need to consider the different stages involved: heating the ice to 0°C, melting the ice to water at 0°C, heating the water to 100°C, boiling the water to steam at 100°C, and then heating the steam from 100°C to the final temperature of 124°C.
Let's break down the calculation step by step:
1. Heating the ice to 0°C:
We will use the specific heat capacity (Cp) of ice, which is given as 2.06 J/g•°C. The change in temperature is from -25°C to 0°C, which is a rise of 25°C. So, the heat required for this step can be calculated as:
Q1 = mass of ice (23.0 g) × cp(ice) x change in temperature (25°C).
2. Melting the ice to water at 0°C:
We will use the heat of fusion (ΔHfus) of ice, which is given as 334 J/g. The mass of ice remains the same, and since it is all converted to water, the heat required for this step can be calculated as:
Q2 = mass of ice (23.0 g) × ΔHfus.
3. Heating the water from 0°C to 100°C:
We will use the specific heat capacity (Cp) of water, which is given as 4.18 J/g•°C. The change in temperature is from 0°C to 100°C, which is a rise of 100°C. So, the heat required for this step can be calculated as:
Q3 = mass of water (equal to the mass of melted ice, 23.0 g) × Cp(water) × change in temperature (100°C).
4. Boiling the water to steam at 100°C:
We will use the heat of vaporization (ΔHvap) of water, which is given as 2260 J/g. The mass of water remains the same, and since it is all converted to steam, the heat required for this step can be calculated as:
Q4 = mass of water (23.0 g) × ΔHvap.
5. Heating the steam from 100°C to the final temperature of 124°C:
We will use the specific heat capacity (Cp) of steam, which is given as 1.99 J/g•°C. The change in temperature is from 100°C to 124°C, which is a rise of 24°C. So, the heat required for this step can be calculated as:
Q5 = mass of steam (equal to the mass of melted ice, 23.0 g) × Cp(steam) × change in temperature (24°C).
Finally, to find the total heat required, we sum up the heat required for each step:
Total heat required = Q1 + Q2 + Q3 + Q4 + Q5.
Substituting the given values into the equations above, you can calculate the total heat required for the process.