Asealed container holds 0.020 moles of nitrogen (n2) gas, at a pressure of 1.5 atmospheres and a temperature of 290 k. the atomic mass of nitrogen is 14.0 g/mol. the boltzmann constant is 1.38 × 10-23 j/k and the ideal gas constant is r = 8.314 j/ mol · k = 0.0821 l · atm/mol · k. the mass density of the gas is closest to

Data:

n = 0.020 moles

Gas: nitrogen (N2) gas

p = 1.5 atm

T = 290 k =

atomic mass of nitrogen = 14.0 g/mol.

the boltzmann constant is 1.38 × 10-23 j/k (it is not required to solve this problem)

ideal gas constant, R = 8.314 j/ mol · k = 0.0821 l · atm/mol · k.

Question: the mass density of the gas

Solution:

Formulas:

pV = nRT

mass density = mass / volume

mass = n * molar mass

molar mass = 2 * atomic mass = 2 * 14.0 g/mol = 28.0 g / mol

mass = 0.020 mol * 28 g/mol = 0.56 g

pV = nRT => V = nRT / p = 0.020 mol * 0.0821 (atm*l /K*mol) * 290K / 1.5 atm

V = 0.3175 liter = 317.5 ml

density = m / V = 0.56 g / 317.5 ml = 0.0018 g/ml = 0.0018 kg / l = 1.8 kg / m^3

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