given the following info for water molar heat of fusion 6.02kj/mol calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
q1 = heat released when steam vapor @ 100 C is condensed to liquid water @ 100 C.
q1 = mass steam x heat vaporization
q2 = heat released in cooling liquid water from 100 C to zero C.
q2 = mass water x specific heat water x (Tfinal-Tinitial).
q3 = heat released changing liquid water at zero C to ice at zero C.
q3 = mass water x heat fusion
q4 = heat released in cooling ice from zero C to ice at -50 C.
q4 = mass ice x specific heat ice x (Tfinal-Tinitial)
Total Q = q1 + q2 + q3 + q4.
To calculate the total quantity of heat evolved, we need to consider the heat involved in each step of the process: condensation, cooling, and freezing. Let's break it down step by step:
1. Condensation: The heat involved in condensation is the heat of vaporization, which is the same as the heat of fusion but with a negative sign since it is the opposite process. The molar heat of fusion given is 6.02 kJ/mol. However, we need to convert the mass of water to moles.
The molar mass of water (H2O) is 18.02 g/mol. We can now calculate the moles of water present in 10.0 g:
moles = mass / molar mass
moles = 10.0 g / 18.02 g/mol
2. Cooling: To calculate the heat involved in cooling, we need to consider the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g·°C. We will convert the temperature change to Celsius.
The initial temperature of steam is 100 °C (boiling point of water at atmospheric pressure). The final temperature is -50 °C, so the temperature change is:
temperature change = final temperature - initial temperature
temperature change = -50 °C - 100 °C
3. Freezing: The heat involved in freezing is the same as the heat of fusion. Since the water is already at the freezing point (-50 °C), there is no temperature change during freezing.
Now we can calculate the total quantity of heat evolved using the formulas:
1. Condensation: heat_condensation = moles × molar heat of fusion
2. Cooling: heat_cooling = mass × specific heat capacity × temperature change
3. Freezing: heat_freezing = moles × molar heat of fusion
Finally, we can add these three values to get the total quantity of heat evolved:
total heat evolved = heat_condensation + heat_cooling + heat_freezing
By plugging in the calculated values, you can find the answer.