Question

The density of a gas is 1.76g/L at 1 atm and 10 °C. What is its density at 1.5 atm and 20 °C?

A. 4.65g/L

B. 3.23g/L

C. 1.52g/L

D. 2.15g/L

E. 2.55g/L

Answer 1

We know that PV = nRT

                             = ( m/M ) RT

                         P = ( m/V ) * ( RT / M )

                         P = (dRT) /M

                         d = ( PM)/(RT)

Where

d = density

T = Temperature

P = pressure

M = Molar mass

R = gas constant = 0.0821 L atm / mol - K

m = mass of the gas

V= Volume of the gas

Since the gas is the same M will not change and R will also a constant

therefore d is proportional to (P/T)

OR       d₁ / d₂ = (P₁T₂)/(P₂T₁)

Where

d₁ = initial density = 1.76 g/L

P₁ = initial pressure = 1 atm

T₁ = initial temperature = 10^oC = 10+ 273 = 283 K

d₂ = final density = ?

P₂ = final pressure = 1.5 atm

T₂=final temperature = 20^oC = 20+ 273 = 293 K

Plug the values we get d₂ = (d₁P₂T₁)/((P₁T₂)

                                      = (1.76*1.5*283) / (1*293)

                                      = 2.55 g/L

Therefore option (E) is correct