A sample of hydrogen gas (H2) was found to effuse at a rate equal to 6.7 times that of an unknown gas. The molecular weight of the unknown gas is __________ g/mol. Express your answer to one (tenth) decimal place.

I would make up a rate for the unknown gas and multiply that made up rate x 6.7 to find the rate of H2. Plug in those numbers.

rate1/rate2 = sqrt(M2/M1)
Solve for M (depending upon what you call rate 1 and rate2, M2 and M1.

To solve this problem, we need to use Graham's Law of Effusion, which relates the rate of effusion of two gases to their respective molecular weights.

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight.

Mathematically, we can express it using the equation:

(Rate of effusion of gas A) / (Rate of effusion of gas B) = sqrt(Molecular weight of gas B) / sqrt(Molecular weight of gas A)

Let's apply this equation to the problem.

Given:
Rate of effusion of hydrogen gas (H2) = 6.7 times rate of effusion of unknown gas

We can set up the equation as follows:

6.7 = sqrt(Molecular weight of unknown gas) / sqrt(Molecular weight of hydrogen gas)

We know that the molecular weight of hydrogen gas (H2) is approximately 2 g/mol (1 g for each hydrogen atom).

Plugging in this information, we get:

6.7 = sqrt(Molecular weight of unknown gas) / sqrt(2 g/mol)

Simplifying the equation, we can cross-multiply and square both sides:

(6.7)^2 = (sqrt(Molecular weight of unknown gas))^2 / (sqrt(2 g/mol))^2

44.89 = Molecular weight of unknown gas / 2 g/mol

Multiplying both sides by 2 g/mol, we get:

2 g/mol * 44.89 = Molecular weight of unknown gas

Molecular weight of unknown gas = 89.78 g/mol

Therefore, the molecular weight of the unknown gas is approximately 89.8 g/mol when rounded to one decimal place.