Fluid Leak Calculation in a 40L Vessel

The kilograms of fluid lost due to the leak

The kilograms of fluid lost due to the leak in a 40L vessel containing a fluid is 4.2 grams.

To determine the kilograms of fluid lost due to the leak, we need to use the ideal gas law equation, which states:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Assuming the fluid is a gas, we can use this equation to calculate the number of moles of gas in the container at the initial conditions. We can then use the same equation to calculate the number of moles of gas in the container after the leak has occurred, using the new pressure and temperature values.

Once we have the number of moles of gas before and after the leak, we can calculate the difference and convert it to kilograms using the molar mass of the fluid. For example, if the fluid is nitrogen gas (N₂) at an initial temperature of 25°C and pressure of 1 atm, we can calculate the number of moles of gas using:

PV = nRT

(1 atm)(40 L) = n(0.0821 L atm/mol K)(298 K)

n = 1.64 mol

If the leak is discovered and the temperature drops to 20°C and pressure drops to 0.9 atm, we can calculate the number of moles of gas using:

PV = nRT

(0.9 atm)(40 L) = n(0.0821 L atm/mol K)(293 K)

n = 1.49 mol

The difference in moles is 0.15 mol, which we can convert to kilograms using the molar mass of nitrogen gas (28 g/mol):

0.15 mol x 28 g/mol = 4.2 g

Therefore, the amount of nitrogen gas lost due to the leak is 4.2 grams.