To calculate the mass of nitrogen dissolved in the aquarium, we first need to calculate the concentration of nitrogen in the water using Henry's Law.
Henry's Law states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid. The equation for Henry's Law is:
C = k * P
where:
C = concentration of the gas in the liquid (in M)
k = Henry's Law constant (in M/atm)
P = partial pressure of the gas above the liquid (in atm)
Given that the mole fraction of nitrogen is 0.78 and the total pressure is 1.0 atm, we can calculate the partial pressure of nitrogen to be:
P(N2) = 0.78 * 1.0 atm = 0.78 atm
Now we can use Henry's Law to calculate the concentration of nitrogen in the water:
C(N2) = (6.1 × 10^-6 M/atm) * (0.78 atm) = 4.758 × 10^-6 M
Next, we convert the concentration to moles of nitrogen using the volume of the aquarium:
moles of N2 = concentration * volume
moles of N2 = 4.758 × 10^-6 M * 90.0 L = 4.2822 x 10^-4 moles
Finally, we can convert moles of nitrogen to grams:
mass = moles * molar mass of nitrogen
mass = 4.2822 x 10^-4 moles * 28.02 g/mol = 0.012 g
Therefore, the mass of nitrogen dissolved in the 90.0 L home aquarium at room temperature is 0.012 grams.
Calculate the mass of nitrogen dissolved at room temperature in an 90.0 L home aquarium. Assume a total pressure of 1.0 atm and a mole fraction for nitrogen of 0.78. The Henry's law constant for nitrogen at 25 °C is 6.1 × 10-* M/atm
Express your answer in grams to two significant figures.
1 answer