Question

A sealed 51 m³ tank is filled with 9000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 330 K. The atomic mass of oxygen is 16.0 g/mol. The mass density of the oxygen gas, in SI units, is closest to

11

4.2

5.6

2.8

7.1

Answer 1

Here first we need to find out the initial Pressure of the gas.

Use the ideal gas law:

PV = nRT

Solve for P:

P = nRT/V

n = 9000 moles

R = 8.314 m³·Pa·K^-1·mol^-1

T= 270 K
(use the initial T for initial V)

V = 51 M³

P = (9000 molesx 8.314 m³·Pa·K^-1·mol^-1 x 270 K)/51 = 396137.647 Pa

Now, as we know that,

density=m/ V = m(1/V) = m (P/nRT) = (m/n) (P / RT) = MWt (P/ RT)

MWt is the molecular weight of the compound (m/nm/n) in g/mol, Here The atomic mass of oxygen is 16.0 g/mol.

Now, density = MWt (P/ RT) = 16.0 g/mol( 396137.647 x 8.314 m³·Pa·K^-1·mol^-1 x 270 K) = 2823.53 = 2.8 kg/m³ -Ans