Question

Five grams of chlorine gas are contained in a cylindrical container. The gas is at room temperature (298K) and pressure (1 atm). The molecular weight of chlorine is 35.45 g/mole. Assume the chlorine gas is an ideal gas. The height of the container is 2 cm. What is the radius of the container?

Answer 1

For radius of a cylnder:

V = A*h

A = PI*(R)^2

so

V = A*PI*R^2

Apply ideal gas Law for volume

PV = nRT

V = nRT/P

NOTE that chlorine gas is DIATOMIC, meaning it is actually a molecule with 2 atoms of Cl

MW Chlroine gass = 35.45 *2 = 70.9 g/mol

n = mass/MW = 5/70.9 = 0.071428 mol of Chlorine gas

V = nRT/P

V = (0.071428 )(0.082*298)/(1) = 1.74541 L

We need to change this to m3 so

V = 1.7454/1000 = 1.7454*10^-3 m3

then

V = h*PI*R^2

1.7454*10^-3 = (2*10^-2)(3.141592)(R^2)

Solve for radius

R = sqrt((1.7454*10^-3)/( (2*10^-2)(3.141592)))

R = 0.846m = 84 cm