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
1.1g
To calculate the mass of nitrogen dissolved in an 80L home aquarium, we need to use the ideal gas law and the concept of mole fraction.
The ideal gas law states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
- Total pressure (P) = 1 atm
- Volume (V) = 80 L
- Mole fraction of nitrogen (X) = 0.78
First, let's find the number of moles of nitrogen in the aquarium. To do that, we need to calculate the partial pressure of nitrogen using the mole fraction.
The partial pressure of nitrogen (P(N2)) can be calculated as:
P(N2) = X * P
Substituting the given values:
P(N2) = 0.78 * 1 atm
P(N2) = 0.78 atm
Now, let's convert the partial pressure to moles using the ideal gas law. Rearranging the ideal gas law equation, we get:
n = PV / RT
Substituting the values:
n(N2) = (0.78 atm) * (80 L) / (0.0821 L⋅atm/mol⋅K) * (room temperature in Kelvin)
Assuming room temperature to be around 25°C or 298 K, we substitute that value:
n(N2) = (0.78 atm) * (80 L) / (0.0821 L⋅atm/mol⋅K) * (298 K)
Calculating this expression will give us the number of moles of nitrogen. Finally, to find the mass of nitrogen, we need to use the molar mass of nitrogen, which is approximately 28 g/mol.
Mass(N2) = n(N2) * molar mass(N2)
Substituting the value of the number of moles (n(N2)) and the molar mass of nitrogen, we can calculate the mass of nitrogen dissolved in the aquarium at room temperature.
Please note that if the composition of gases in the aquarium changes or if the temperature or pressure deviate significantly from standard conditions, the calculation may vary.