How many kilojoules of energy would be liberated by condensing 48.03 mol of steam initially at 110.0 °C and then allowing the liquid to cool to 32.9 °C?
you have three factors;
heat to remove to cool steam to 100C:
heat to condense steam at 100C:
heat to remove to cool water from 100 to 32.9C.
I assume you can do these, you may not have the heats of vaporization and specific heats in mole units, if not, convert 48.03 moles to kg.
To determine the amount of energy liberated by condensing the steam, you will need to calculate the change in enthalpy (∆H) during this process.
The formula to calculate ∆H is as follows:
∆H = mc∆T
where:
m is the mass of the substance (in this case, steam)
c is the specific heat capacity of the substance (in this case, steam)
∆T is the change in temperature
To calculate the change in enthalpy during the condensation process, follow these steps:
1. Convert the given number of moles (48.03 mol) of steam into grams. To do this, multiply the number of moles by the molar mass of water (H2O), which is approximately 18.015 g/mol:
Mass = Number of moles × Molar mass
= 48.03 mol × 18.015 g/mol
2. Calculate the initial enthalpy (before condensation) using the formula:
H1 = mc∆T
where m is the mass of the substance (in grams), c is the specific heat capacity of steam, and ∆T is the change in temperature. The specific heat capacity of steam is approximately 4.18 J/g·°C.
∆T = (final temperature - initial temperature)
= (32.9 °C - 110.0 °C)
H1 = m × c × ∆T
3. Calculate the final enthalpy (after condensation) using the same formula as above, but with the final temperature. In this case, the final temperature is the boiling point of water, which is 100.0 °C.
∆T = (final temperature - initial temperature)
= (100.0 °C - 110.0 °C)
H2 = m × c × ∆T
4. Calculate the change in enthalpy (∆H) by subtracting the initial enthalpy (H1) from the final enthalpy (H2):
∆H = H2 - H1
5. Finally, convert the change in enthalpy from joules (J) to kilojoules (kJ) by dividing the value obtained by 1000.
By following these steps, you will be able to determine the amount of energy liberated by condensing the given amount of steam.