A cylinder 1.00 m tall with inside diameter 0.120 m is used to hold propane gas (molar mass 44.1 g/mol). It is initially filled with gas until the gauge pressure is 1.30 x 106 Pa and the temperature is 22.0oC. The temperature of the gas remains constant as it is partially emptied out of the tank, until the gauge pressure is 2.50 x 105 Pa. Calculate the mass of propane that has been used.

To calculate the mass of propane that has been used, we need to use the ideal gas law equation and the given information.

The ideal gas law equation is:

PV = nRT

Where:
P = pressure of the gas (in Pa)
V = volume of the gas (in m^3)
n = number of moles of the gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas (in Kelvin)

First, we need to convert the given temperature from Celsius to Kelvin:
T1 = 22.0°C + 273.15 = 295.15 K
T2 = 22.0°C + 273.15 = 295.15 K

Given:
P1 = 1.30 x 10^6 Pa
P2 = 2.50 x 10^5 Pa
V = π * (d/2)^2 * h

Inside diameter of the cylinder (d) = 0.120 m
Height of the cylinder (h) = 1.00 m

Substituting the given values into the equation, we can calculate the initial number of moles (n1) using P1 and T1:

n1 = (P1 * V) / (R * T1)

Substituting the given values, we get:
n1 = (1.30 x 10^6 Pa) * π * (0.120/2)^2 * 1.00 m / (8.314 J/(mol·K) * 295.15 K)

Next, we can calculate the final number of moles (n2) using P2 and T2:

n2 = (P2 * V) / (R * T2)

Substituting the given values, we get:
n2 = (2.50 x 10^5 Pa) * π * (0.120/2)^2 * 1.00 m / (8.314 J/(mol·K) * 295.15 K)

Finally, we can calculate the mass of propane used (Δm) by subtracting n2 from n1 and multiplying by the molar mass of propane (44.1 g/mol):

Δm = (n1 - n2) * molar mass

Substituting the calculated values, we get:
Δm = (n1 - n2) * 44.1 g/mol

By following these steps and substituting the given values, you can calculate the mass of propane that has been used.