Complete Question
A gas storage cylinder in an ordinary chemical laboratory measures 3.5 cm wide and 9.2 cm high with this label on it:
Contents: N2 Gas
Pressure 18.6 atm
If the cylinder is opened and the gas allowed to escape into a large empty plastic bag, what will be the final volume of nitrogen gas, including what’s collected in the plastic bag and what’s left over in the cylinder?
Use 1 atm for the gas final pressure
Answer:
The final volume is 1647.03cm³ or 1.65 litres
Explanation:
Given
Width of cylinder, W = 3.5 cm
Height of Cylinder, H = 9.2 cm
Gas Initial Pressure, P1 = 18.6 atm
Gas Final Pressure, P2 = 1 atm
First, the initial volume of gas has to be calculated to known the quantity of gas before gas outflow
Volume of Gas, V = Volume of a cylinder
V = πr²h
Given the the width of the cylinder is 3.5cm
This means that the diameter of the cylinder is also 3.5cm
Hence; Diameter, D = 3.5cm
Radius, r = ½D
r = ½ * 3.5cm
r = 1.75cm
So, V1 = πr²h becomes
V1 = π * 1.75² * 9.2
V1 = 28.175π cm³
V1 = 88.55 cm³
From Ideal Gas Law;
PV = nRT
Where k = PV (From Boyle's Law)
P1V1 = P2V2 ---- Make V2 the subject of formula
V2 = (P1V1)/P2
Where P1,P2,V1 and V2 represent the initial pressure, final pressure, initial volume and final volume, respectively.
Recall that P1 = 18.6 atm
P2 = 1 atm
V1 = 88.55 cm³
Final volume, V2 = (P1V1)/P2
V2 = (18.6 atm * 88.55 cm³)/1 atm³
V2 = 1647.03cm³
Convert to Litre
V2 = 1647.03/1000
V2 = 1.64703 litres
V2 = 1.65 L
Hence, the final volume is 1647.03cm³ or 1.65litres
