what is the ratio of effusion for f₂ gas to cl₂ gas?\na f₂ effuses 1.87 times faster\nb f₂ effuses 1.37…

Explanation:

Step1: Recall Graham's law of effusion

The rate of effusion of a gas is inversely proportional to the square - root of its molar mass. The formula is $\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}$, where $r_1$ and $r_2$ are the rates of effusion of two gases and $M_1$ and $M_2$ are their molar masses. Let gas 1 be $F_2$ and gas 2 be $Cl_2$. The molar mass of $F_2$ ($M_{F_2}$) is $M_{F_2}=2\times19.0\ g/mol = 38.0\ g/mol$, and the molar mass of $Cl_2$ ($M_{Cl_2}$) is $M_{Cl_2}=2\times35.45\ g/mol=70.9\ g/mol$.

Step2: Calculate the ratio of effusion rates

Substitute the molar masses into Graham's law formula: $\frac{r_{F_2}}{r_{Cl_2}}=\sqrt{\frac{M_{Cl_2}}{M_{F_2}}}=\sqrt{\frac{70.9}{38.0}}\approx\sqrt{1.866}\approx1.37$.

Answer:

B. $F_2$ effuses 1.37 times faster