Answer:
The concentration of mercury (Hg) in the room saturated with mercury vapor at 79°F is approximately 5.99 ppm.
Step-by-step explanation:
To find the concentration of mercury (Hg) in parts per million (ppm) in a 500 ft³ room saturated with mercury vapor at 79°F, you can use the ideal gas law and the vapor pressure of mercury.
First, convert the temperature from Fahrenheit (°F) to Kelvin (K):
T(K) = (T(°F) - 32) × 5/9 + 273.15
T(K) = (79°F - 32) × 5/9 + 273.15 ≈ 298.15 K
Now, use the ideal gas law to find the number of moles of mercury vapor in the room:
PV = nRT
Where:
P = Pressure (vapor pressure of mercury) = 0.0002 mmHg (convert to atm)
V = Volume = 500 ft³ (convert to liters)
n = Number of moles
R = Ideal gas constant = 0.0821 L·atm/mol·K
T = Temperature in Kelvin (298.15 K)
Convert pressure from mmHg to atm:
1 mmHg = 0.00131579 atm
0.0002 mmHg = 0.0002 × 0.00131579 atm ≈ 2.63158 × 10^-7 atm
Now, plug in these values:
(2.63158 × 10^-7 atm) * (V = 500 ft³ * 28.3168 L/ft³) = n * (0.0821 L·atm/mol·K) * (298.15 K)
Solve for n (number of moles):
n ≈ (2.63158 × 10^-7 atm * 500 ft³ * 28.3168 L/ft³) / (0.0821 L·atm/mol·K * 298.15 K)
n ≈ 0.000003377 moles
Now that you have the number of moles of mercury vapor in the room, you can calculate the concentration in ppm.
1 ppm = 1 part per million, which is equivalent to 1 mole of solute per 1 million moles of solution.
Concentration (ppm) = (moles of solute / moles of solution) * 1,000,000
Concentration (ppm) = (0.000003377 moles / (0.000003377 moles + moles of air in the room)) * 1,000,000
Since air is mostly composed of nitrogen and oxygen and we assume it behaves ideally, you can use the ideal gas law to estimate the moles of air in the room. At standard conditions (1 atm and 298.15 K), 1 mole of any ideal gas occupies approximately 22.4 liters. Therefore:
moles of air = (P * V) / (R * T)
moles of air = (1 atm * 500 ft³ * 28.3168 L/ft³) / (0.0821 L·atm/mol·K * 298.15 K)
Now, calculate the concentration:
Concentration (ppm) = (0.000003377 moles / (0.000003377 moles + moles of air)) * 1,000,000
Calculate moles of air first:
moles of air ≈ (1 atm * 500 ft³ * 28.3168 L/ft³) / (0.0821 L·atm/mol·K * 298.15 K)
moles of air ≈ 564.49 moles
Now calculate the concentration:
Concentration (ppm) = (0.000003377 moles / (0.000003377 moles + 564.49 moles)) * 1,000,000
Concentration (ppm) ≈ (0.000003377 / (0.000003377 + 564.49)) * 1,000,000 ≈ 5.99 ppm
So, the concentration of mercury (Hg) in the room saturated with mercury vapor at 79°F is approximately 5.99 ppm.