40000liter gasoline tank is filled with liquid gasoline with an avg vapor pressure of 20 mm Hg.At 50% saturation, what weight of gasoline would escape to the atmosphere during filling?

To determine the weight of gasoline that would escape to the atmosphere during filling, we need to calculate the weight of the gasoline vapor that escapes.

First, we need to convert the given vapor pressure from mm Hg to a unit that is commonly used in calculations, such as kilopascals (kPa). The conversion between mm Hg and kPa is as follows:

1 mm Hg = 0.133 kPa

Therefore, 20 mm Hg = 20 x 0.133 kPa = 2.66 kPa

Next, we need to calculate the total pressure of the gas in the tank. The total pressure is the sum of the vapor pressure and the pressure exerted by the liquid gasoline. Since the tank is filled to 50% saturation, the pressure exerted by the liquid gasoline is equal to the vapor pressure.

Total pressure = Vapor pressure + Pressure exerted by liquid gasoline
Total pressure = 2.66 kPa + 2.66 kPa = 5.32 kPa

Now, we can use the ideal gas law to calculate the weight of the escaped gasoline vapor. The ideal gas law equation is:

PV = nRT

Where:
P = pressure (in pascals)
V = volume of gas (in cubic meters)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in kelvin)

First, we need to convert the volume of the gasoline tank from liters to cubic meters. Since 1 liter is equal to 0.001 cubic meters, the volume of the tank in cubic meters is:
40,000 liters x 0.001 m^3/liter = 40 m^3

Assuming the temperature remains constant, we can rearrange the ideal gas law equation to solve for the number of moles of gas:

n = PV / RT

Where:
P = Total pressure (in pascals) = 5.32 kPa x 1000 Pa/kPa = 5320 Pa
V = Volume of gas (in cubic meters) = 40 m^3
R = Ideal gas constant = 8.314 J/(mol·K)
T = Temperature (in kelvin)

Now we can calculate the number of moles of gas using the equation:

n = (5320 Pa)(40 m^3) / (8.314 J/(mol·K))(T in kelvin)

Finally, we can calculate the weight of the escaped gasoline vapor using the molar mass of gasoline, which is approximately 114 grams/mol. We use the equation:

Weight = Moles of gas x Molar mass of gas

Weight = n (from previous step) x 114 grams/mol

The resulting weight will be the weight of gasoline that escapes to the atmosphere during filling.