Final answer:
To find the concentration of nitrous oxide in the atmosphere in parts per million (ppm), we need to convert the mole fraction to a partial pressure and then calculate the concentration using the ideal gas law.
Step-by-step explanation:
To find the concentration of nitrous oxide in the atmosphere in parts per million (ppm), we need to convert the mole fraction to a partial pressure and then calculate the concentration using the ideal gas law. The mole fraction of nitrous oxide can be converted to a partial pressure by multiplying it by the total pressure of the atmosphere. Let's assume the total pressure of the atmosphere is 1 atm. So, the partial pressure of nitrous oxide is (1 atm) * (1.818 × 10^-5) = 1.818 × 10^-5 atm.
Next, we can use the ideal gas law equation: PV = nRT, where P is the partial pressure in atm, V is the volume in L, n is the number of moles, R is the ideal gas constant (0.0821 L.atm/mol.K), and T is the temperature in Kelvin. Rearranging the equation to solve for n, we have n = PV / RT.
Since we are looking for the concentration of nitrous oxide in ppm, we need to divide the number of moles of nitrous oxide by the total number of moles in the atmosphere and multiply by 1,000,000 (ppm = parts per million).
Using the information provided, we can calculate the concentration:
n(NO) = (1.818 × 10^-5 atm) * (1.00 L) / (0.0821 L.atm/mol.K * 273 K)
n(N₂) = 0.78 atm * 1.00 L / (0.0821 L.atm/mol.K * 273 K)
n(O₂) = 0.21 atm * 1.00 L / (0.0821 L.atm/mol.K * 273 K)
Once we have the number of moles of nitrous oxide, we can calculate the concentration in ppm using the equation:
Concentration(NO) = (n(NO) / (n(NO) + n(N₂) + n(O₂))) * 1,000,000
Calculating the values above will give you the concentration of nitrous oxide in the atmosphere in ppm.