How much energy (in kilojoules) is released when 12.8 g of steam at 130.0 C is condensed to give liquid water at 73.5 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 steam moving from 130 C to 100 C.

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

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

q3 = heat released in moving liquid water from 100 C to 73.5 C.
q3 = mass water x specific heat water x (Tfinal-Tinitial).

Total q = q1 + q2 + q3

To calculate the energy released when the steam is condensed, we need to consider two components:

1. Energy required to cool the steam from 130.0°C to 100.0°C.
2. Energy released when the steam condenses from 100.0°C to 73.5°C.

Let's calculate both components step-by-step:

Step 1: Calculate the energy required to cool the steam from 130.0°C to 100.0°C.

First, we need to calculate the heat capacity of steam:

Heat capacity of vapor = 33.6 J/(K*Mol)

Next, we calculate the moles of steam:

Molar mass of water (H2O) = 18.02 g/mol

Moles of steam = mass of steam / molar mass of water
= 12.8 g / 18.02 g/mol
≈ 0.710 mol

Now, we can calculate the energy required to cool the steam from 130.0°C to 100.0°C using the heat capacity of the vapor:

Energy = heat capacity * moles * change in temperature

Energy = 33.6 J/(K*Mol) * 0.710 mol * (100.0°C - 130.0°C)

Step 2: Calculate the energy released when the steam condenses from 100.0°C to 73.5°C.

To calculate this component, we need to use the heat of vaporization of liquid water:

Heat of vaporization = 40.67 kJ/mol

The number of moles of steam that condense can be calculated using the molar heat capacity of liquid water:

Molar heat capacity of liquid water = 75.3 J/(K*Mol)

Molar heat capacity of liquid water = heat of vaporization * moles

Moles of steam that condense = molar heat capacity of liquid water / heat of vaporization

Moles of steam that condense = (75.3 J/(K*Mol) / (40.67 kJ/mol) * 1000 J/kJ

Finally, we can calculate the energy released when the steam condenses:

Energy = heat of vaporization * moles

Energy = 40.67 kJ/mol * moles

Add the energy from step 1 and step 2 together to get the total energy released when the steam is condensed:

Total energy released = Energy from step 1 + Energy from step 2

Please note that the calculations assume that there is no heat loss to the surrounding environment during the process.

To calculate the energy released when steam is condensed, we need to consider the energy change during both cooling and phase change.

First, we need to calculate the energy required to cool down the steam from 130.0°C to 100.0°C. To do this, we will use the formula:

Q = m * C * ΔT

Where:
Q is the energy in joules
m is the mass of the substance in grams (12.8 g)
C is the molar heat capacity in J/(K*Mol) (33.6 J/(K*Mol) for the vapor phase, as given)
ΔT is the change in temperature in Kelvin (130.0°C to 100.0°C = 30.0 K)

Converting molar heat capacity from J/(K*Mol) to J/(K*g):
C_vapor = 33.6 J/(K*Mol) / (18.015 g/Mol) = 1.866 J/(K*g)

Now we can calculate the energy required for cooling:

Q_cooling = m * C_vapor * ΔT
Q_cooling = 12.8 g * 1.866 J/(K*g) * 30.0 K = 680.2944 J

Next, we need to calculate the energy released during the phase change from steam to liquid water. The heat of vaporization of liquid water is given as 40.67 kJ/mol.

Converting heat of vaporization from kJ/mol to J/g:
ΔH_vaporization = 40.67 kJ/mol / (18.015 g/Mol) = 2.256 kJ/g

Now we can calculate the energy released during the phase change:

Q_phase_change = m * ΔH_vaporization
Q_phase_change = 12.8 g * 2.256 kJ/g = 28.9248 kJ = 28924.8 J

Finally, we can calculate the total energy released:

Total energy released = Q_cooling + Q_phase_change
Total energy released = 680.2944 J + 28924.8 J = 29605.0944 J

Converting the total energy released from joules to kilojoules:

Total energy released = 29605.0944 J / 1000 = 29.6051 kJ

Therefore, approximately 29.605 kJ of energy is released when 12.8 g of steam at 130.0°C is condensed to give liquid water at 73.5°C.