You compress air saturated with water vapor at 24°C and atmospheric pressure (101.325 kPa) until the total

pressure is doubled and the temperature is 36°C. What is the final pressure of the water vapor?

To find the final pressure of the water vapor, we need to use the concept of partial pressure and the relationship between pressure and temperature known as Charles's Law.

Here's how you can calculate the final pressure of the water vapor:

1. Convert the temperatures to Kelvin scale:
Initial temperature (T1) = 24°C + 273.15 = 297.15 K
Final temperature (T2) = 36°C + 273.15 = 309.15 K

2. Determine the initial partial pressure of the water vapor (P1):
Since the air is saturated with water vapor, the partial pressure of the water vapor is equal to the vapor pressure at 24°C. You can find this value in a vapor pressure table. Let's assume it is P1 = X kPa.

3. Calculate the initial total pressure (P_total1):
The initial total pressure is given as atmospheric pressure, which is 101.325 kPa.

4. Use Charles's Law to determine the final total pressure (P_total2):
Charles's Law states that the ratio of the initial and final volumes is equal to the ratio of the initial and final temperatures, assuming constant pressure.
P_total1 / T1 = P_total2 / T2

Substituting the values:
101.325 kPa / 297.15 K = P_total2 / 309.15 K

Solving for P_total2:
P_total2 = (101.325 kPa / 297.15 K) * 309.15 K

5. Find the final partial pressure of the water vapor (P2):
Since the total pressure is equal to the sum of the partial pressures of all the gases present, we can calculate the final partial pressure using the equation:
P_total2 = P2 + P_other_gases

Rearranging the equation:
P2 = P_total2 - P_other_gases

P_other_gases = P_total1 - P1

Substituting the values:
P_other_gases = 101.325 kPa - X kPa

P2 = P_total2 - (101.325 kPa - X kPa)

6. Simplify and solve for P2:
P2 = P_total2 - 101.325 kPa + X kPa

Substitute the value of P_total2 from step 4 and we have our final answer.

By following these steps, you can determine the final pressure of the water vapor in the compressed air.