Final answer:
NO effuses approximately 1.238 times faster than NO₂ at a fixed temperature, according to Graham's law of effusion. The closest simple fraction is 4:3, which is closer to a 1:1 ratio, making option A (1:1) the closest given answer choice.
Step-by-step explanation:
The question is asking to compare the rates of effusion of two different gases, nitric oxide (NO) and nitrogen dioxide (NO₂), at a fixed temperature. According to Graham's law of effusion, the rate of effusion for a gas is inversely proportional to the square root of its molar mass. The formula representing Graham's law is:
Rate of effusion of gas 1 / Rate of effusion of gas 2 = √(Molar mass of gas 2 / Molar mass of gas 1)
Looking at the molar masses, NO has a molar mass of approximately 30 g/mol, and NO₂ has a molar mass of approximately 46 g/mol. Using Graham's law:
Rate of NO / Rate of NO₂ = √(46 / 30) = √(1.533) ≈ 1.238
So NO effuses approximately 1.238 times faster than NO₂. However, the closest simple fraction that represents this ratio is 4:3, which is closer to 1:1, none of the provided answer choices exactly match our calculation. If we had to choose the closest answer, it would be option A. 1:1.