Final answer:
Using Graham's Law of Effusion, the effusion rate of a homonuclear diatomic gas that effuses 3.73 times faster than N2 indicates the gas is hydrogen with a chemical formula of H2.
Step-by-step explanation:
The student is asking about the chemical formula of a homonuclear diatomic gas that effuses 3.73 times faster than nitrogen gas (N2). The principle involved in answering this question is Graham's Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be expressed as (rate of effusion of A)/(rate of effusion of B) = sqrt(molar mass of B/molar mass of A).
Nitrogen gas, N2, has a molar mass of 28 g/mol. Using Graham's Law, if a gas effuses 3.73 times as fast as N2, its molar mass can be calculated. By rearranging the formula to solve for the molar mass of the unknown gas (molar mass of A), we have molar mass of A = (1/3.73)2 * molar mass of N2 which would equal 2 g/mol. The only homonuclear diatomic molecule with a molar mass of 2 g/mol is hydrogen, H2. Therefore, the chemical formula for the gas is H2.