Final answer:
The rate of effusion of NO₂ is approximately 1.18 times faster than that of SO₂ when compared at the same temperature and pressure, according to Graham's law of effusion.
Step-by-step explanation:
To calculate the rate of effusion of NO₂ compared to SO₂ at the same temperature and pressure, you can use Graham's law of effusion. According to this law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This can be expressed with the formula:
Rate of Effusion of Gas 1 / Rate of Effusion of Gas 2 = √(Molar Mass of Gas 2 / Molar Mass of Gas 1)
For NO₂ (Molar Mass = 46.01 g/mol) and SO₂ (Molar Mass = 64.07 g/mol), the formula becomes:
Rate of Effusion of NO₂ / Rate of Effusion of SO₂ = √(64.07 / 46.01)
By calculating, we get:
Rate of Effusion of NO₂ / Rate of Effusion of SO₂ ≈ 1.18
Therefore, NO₂ will effuse approximately 1.18 times faster than SO₂ under identical conditions of temperature and pressure.