How much energy (in kilojoules) is released when 15.2g of steam at 114.5∘C is condensed to give liquid water at 63.5∘C? The heat of vaporization of liquid water is 40.67 kJ/mol, and the molar heat capacity is 75.3 J/(K⋅mol) for the liquid and 33.6 J/(K⋅mol) for the vapor.

q1 = heat released in moving T of steam from 114.5 C to 100 C.

q1 = mass steam x specific heat steam x (Tfinal-Tinitial)

q2 = heat released by condensing steam at 100 C to liquid water at 100 C.
q2 = mass steam x heat vaporization/condensation

q3 = heat released by cooling from 100 C to 63.5 C.
q3 = mass H2O x specific heat H2O x (Tfinal-initial)

Total = q1 + q2 + q3.
Note: Make sure your units for mass and specific heat are the same; i.e., if you use mass in grams then you want specific heat in J/g. If you use specific heat in J/mol, you must use mass in mols.

I keep getting 5651.072 kJ.

To calculate the energy released when steam is condensed to liquid water, we need to consider two steps: heating the steam to its boiling point and then condensing it into liquid water.

Step 1: Heating the steam to its boiling point (114.5∘C).
To calculate the energy required to heat the steam, we will use the equation:

q1 = m * C * ΔT

where
q1 is the energy (in kilojoules),
m is the mass of the steam (in grams),
C is the molar heat capacity (in J/(K⋅mol)),
and ΔT is the change in temperature (in Kelvin).

First, we need to convert the mass of the steam to moles by dividing it by the molar mass of steam.

Molar mass of steam = 18.01528 g/mol

moles of steam = mass of steam / molar mass of steam

Next, we need to calculate the change in temperature:

ΔT1 = boiling point of steam - initial temperature
ΔT1 = 114.5∘C - initial temperature

Now, we can calculate the energy required to heat the steam:

q1 = moles of steam * C * ΔT1

Step 2: Condensing the steam into liquid water (63.5∘C).
To calculate the energy released during condensation, we will use the equation:

q2 = moles of steam * enthalpy of vaporization

The enthalpy of vaporization is given as 40.67 kJ/mol, but we need to convert it to J/mol:

enthalpy of vaporization = 40.67 kJ/mol * 1000 J/kJ

Finally, we can calculate the total energy released:

total energy released = q1 + q2

Now let's plug in the given values and calculate the energy.

1. Convert the mass of steam to moles:

moles of steam = 15.2 g / 18.01528 g/mol

2. Calculate the change in temperature for heating the steam:

ΔT1 = 114.5∘C - initial temperature

3. Calculate the energy required to heat the steam:

q1 = moles of steam * C * ΔT1

To get the value of C, we need to calculate the average molar heat capacity using the molar heat capacities for the liquid and vapor phases:

C = (Cliquid + Cvapor) / 2

4. Calculate the energy released during condensation:

q2 = moles of steam * enthalpy of vaporization

5. Calculate the total energy released:

total energy released = q1 + q2

By following the steps above and plugging in the given values, you can determine the energy released when the steam is condensed to liquid water.