You are holding two balloons, an orange balloon and a blue balloon. The orange balloon is filled with neon (Ne) gas and the blue balloon is filled with argon (Ar) gas. The orange balloon has twice the volume of the blue balloon. Which of the following best represents the mass ratio of Ne:Ar in the balloons?

a) 1:1

b) 1:2

c) 2:1

d) 1:3

e) 3:1

a) 1:1

Explanation:

By the ideal gas law:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is temperature.

Both ballons are at the same conditions, so the gases have the same temperature and pressure. The number of moles is the mass (m) divided by the molar mass (Mr). The molar masses are:

Mr (Ne) = 20 g/mol

Mr (Ar) = 40 g/mol

Calling 1 for Ne, and 2 for Ar:

P1*V1 = (m1/20) * R*T1

m1 = 20P1V1/RT1

P2*V2 = (m2/40) * R*T2

m2 = 40P2V2/RT2

V1 = 2V2

m1/m2 = (20P1V1/RT1) / (40P21V2/RT2)

P1 = P2, T1 = T2 so they can be canceled, such as the R:

m1/m2 = 20V1/40V2

m1/m2 = 20*2V2/40V2

m1/m2 = 40V2/40V2

m1/m2 = 1/1

m1:m2 = 1:1