Question

Calculate the mass of nitrogen dissolved at room temperature in an 88.0 L home aquarium. Assume a total pressure of 1.0 atm and a mole fraction for nitrogen of 0.78.

Answer 1

Room temperature is a colloquial expression for the typical or preferred indoor (climate-controlled) temperature to which people are generally accustomed. It represents the small range of temperatures at which the air feels neither hot nor cold, approximately 70 °F (21 °C)

You can use the Ideal Gas law or Henry's law equations:

Calculate partial pressure of gas:

Pg = xg * Pt = 0.78 * 1atm = 0.78 atm

Ideal gas law

PV = nRT

n = PV / RT = (0.78 atm)(88.00 L)/ (0.00821atm/K.mol)(294.15K)

n = 28.42 mol/ 1L

n = (mass N2) / (molar mass)

N2 = 14*2 = 28 amu (g/mol)

mass N2 = n * molar mass

mass N2 = 28.42 mol * 28 gr/mol

mass N2 = 1.0150 grs N2

Henry's law

Sg = kH * Pgas

where kH is the Henry's constant

Sg = 6.1E-4 mol-1 L-1 atm-1 * 0.78 atm

Sg = 4.76E-4 mol/L

4.76E-4 mol / L * 88 L = 0.0418 = 4.18E-2 mol N2

mass N2 = 4.18E-2 mol N2 * 28 g/mol

mass N2 = 1.17 grs N2

Both answers are pretty close for the ideal gas it results mass (1.0150 grs N2) and for Henry's law it results (1.17 grs N2), so you can use as useful.