A gas storage cylinder in an ordinary chemical laboratory measures wide and high. This is the label on it. Contents: gas Pressure: 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

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

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

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