To determine the number of moles of oxygen that had been removed from the cylinder, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's convert the temperature from Celsius to Kelvin by adding 273.15:
T = 24.0 °C + 273.15 = 297.15 K
Next, rearrange the Ideal Gas Law equation to solve for the number of moles:
n = PV / RT
Now, plug in the values:
P₁ = 40.6 atm
P₂ = 38.5 atm
V = 15 L
R = 0.0821 L·atm/(mol·K)
T = 297.15 K
Substitute these values into the equation:
n = (P₁ - P₂) * V / (R * T)
Calculate:
n = (40.6 atm - 38.5 atm) * 15 L / (0.0821 L·atm/(mol·K) * 297.15 K)
n = 2.1 atm * 15 L / (0.0821 L·atm/(mol·K) * 297.15 K)
n = 31.5 L·atm / (2.44 L·atm/(mol·K))
n ≈ 12.91 moles
Therefore, approximately 12.91 moles of oxygen had been removed from the cylinder.