Calculate the mass of nitrogen dissolved at room temperature in an 80L home aquarium. Assume total pressure of 1 atm and mole fraction of .78 for nitrogen

1.3g

To calculate the mass of nitrogen dissolved in an 80L home aquarium at room temperature, we need to consider the ideal gas law and Henry's law.

1. Convert the volume of the aquarium to liters (L):
You have already stated that the volume of the aquarium is 80L, so no conversion is needed.

2. Determine the mole fraction of nitrogen (X) in the aquarium:
Given that the mole fraction of nitrogen is 0.78, we can state that 78% of the total moles of gas in the aquarium is nitrogen.

3. Calculate the partial pressure of nitrogen (P) in the aquarium:
Since the total pressure is 1 atm and the mole fraction of nitrogen is 0.78, we can find the partial pressure of nitrogen using the equation:
P(nitrogen) = Total pressure (1 atm) * Mole fraction of nitrogen (0.78)

P(nitrogen) = 1 atm * 0.78 = 0.78 atm

4. Apply Henry's law to calculate the amount of nitrogen dissolved in the water:
Henry's law states that the amount of gas dissolved in a liquid is proportional to the partial pressure of the gas above the liquid. The constant of proportionality is known as the Henry's law constant (Kh). The equation can be written as:
C = Kh * P
where C is the concentration in mol/L, Kh is the Henry's law constant, and P is the partial pressure of the gas.

The Henry's law constant for nitrogen in water at room temperature is approximately 76.6 L * atm/mol.

C(nitrogen) = Kh * P(nitrogen)
= 76.6 L * atm/mol * 0.78 atm

5. Calculate the moles of nitrogen:
We need to multiply the concentration by the volume in liters to get the number of moles of nitrogen dissolved in the aquarium:
Moles of nitrogen = C(nitrogen) * Volume of the aquarium (80 L)

6. Calculate the mass of nitrogen:
To find the mass of nitrogen, we need to multiply the moles of nitrogen by its molar mass. The molar mass of nitrogen is approximately 28 g/mol.
Mass of nitrogen = Moles of nitrogen * Molar mass of nitrogen (28 g/mol)

So, by following these steps, you can calculate the mass of nitrogen dissolved in the 80L home aquarium at room temperature.