Question

Calculate the mass of nitrogen dissolved at room temperature in an 86.0 L home aquarium. Assume a total pressure of 1.0 atm and a mole fraction for nitrogen of 0.78.

Answer 1

Answer:

Mass of nitrogen gas dissolved= 1.1732 grams

Explanation:

According to Dalton's Law of partial pressure:

$P_{N_2}=P_{Total}X_{N_2}$

Where,

$P_{N_2}$ is the partial pressure of nitrogen

$P_{Total}$ is the Total pressure

$X_{N_2}$ is the mole fraction of nitrogen

Given :

Total pressure  = 1.0 atm

Mole fraction of nitrogen = 0.78

Partial pressure of nitrogen:

$P_{N_2}=1.0\times 0.78 atm$

Partial pressure of nitrogen = 0.78 atm

According to Henry's law:

Solubility = Henry's constant (k)×Partial pressure

k = 6.26×10⁻⁴ mol/L-atm

Thus,

Solubility of nitrogen = 6.26×10⁻⁴ mol/L-atm×0.78 atm = 4.8828×10⁻⁴ mol/L

Given: Volume = 86.0 L

So, Moles of nitrogen gas dissolved:

Moles = Solubility (Concentration dissolved)×Volume

Moles = 4.8828×10⁻⁴ mol/L×86.0 L = 0.0419 moles

Also,

$moles=\frac{Mass(m)}{Molar\ mass (M)}$

$Mass\ of\ nitrogen=moles\times {Molar\ mass}$

Molar mass of nitrogen gas = 28 g/mol

So,

Mass of nitrogen gas dissolved = 0.0419 moles×28 g/mol = 1.1732 grams