Final answer:
The ratio of the average kinetic energy of a SO₂ molecule to that of an O₂ molecule in a mixture of two gases is √2.
Step-by-step explanation:
The ratio of the average kinetic energy of a SO₂ molecule to that of an 0₂ molecule in a mixture of two gases can be determined by using the formula for kinetic energy, which is given by KE = 1/2 mv², where m is the mass of the molecule and v is its velocity.
The average kinetic energy of a molecule is directly proportional to its temperature. Therefore, the ratio of the average kinetic energy of SO₂ to that of 0₂ is equal to the square root of the ratio of their molar masses, since the molar mass of a molecule is directly proportional to its velocity.
The molar mass of SO₂ is approximately 64 g/mol, and the molar mass of O₂ is approximately 32 g/mol. Therefore, the ratio of their average kinetic energies is (√64)/ (√32) = 2/√2 = √2.