The constants for Antoine’s equation for TCE (based on log10 and o
C) are: A= 6.5183, B = 1018.6 and C = 192.7. If a container (negligible volume) is placed in a sealed room 1000 m3 at 30 oC, how many grams of TCE will evaporate upon reaching equilibrium with the liquid and what is the TCE concentration in the room? If the temperature in the room is lowered to 10 oC,
how much TCE will condense and what will be the resulting air concentration?
To calculate the amount of TCE that will evaporate at equilibrium and the TCE concentration in the room, we can use Antoine's equation and the given constants.
1. Calculation at 30°C:
First, convert the temperature from Celsius to Kelvin by adding 273.15:
T1 = 30 + 273.15 = 303.15 K
Now, we can use Antoine's equation to calculate the vapor pressure of TCE at 30°C:
log10(P1) = A - (B / (C + T1))
log10(P1) = 6.5183 - (1018.6 / (192.7 + 303.15))
Next, solve for P1:
P1 = 10^(log10(P1))
Given the container volume and pressure, we can calculate the number of moles of TCE in the gas phase using the ideal gas law:
P1 * V = n * R * T1
Where:
P1 = vapor pressure of TCE at 30°C
V = volume of the container in m3
n = number of moles of TCE
R = ideal gas constant (8.314 J/(mol·K))
T1 = temperature in Kelvin
Solve for n:
n = (P1 * V) / (R * T1)
To convert the number of moles to grams, we need to know the molar mass of TCE (C2HCl3), which is approximately 131.39 g/mol. Multiply the number of moles by the molar mass to get the mass:
mass1 = n * molar mass
Finally, to calculate the TCE concentration in the room, divide the mass of TCE by the room volume:
Concentration1 = mass1 / room volume
2. Calculation at 10°C:
Repeat the same process with the new temperature (10°C) to calculate the amount of TCE that will condense and the resulting air concentration.
T2 = 10 + 273.15 = 283.15 K
log10(P2) = A - (B / (C + T2))
P2 = 10^(log10(P2))
n = (P2 * V) / (R * T2)
mass2 = n * molar mass
Concentration2 = mass2 / room volume
Now you can substitute the values into the equations and perform the calculations to find the desired answers.