Answer: Option d) 37 g
Solution:
This question can be solved using the Graham's Law which states that:
Rate of effusion or diffusion of gas is indirectly proportional to the square root of its Molar Mass.
For two gases A and B, this formula can be written as:
[tex]\frac{r_{a} }{r_{b} } =\sqrt{\frac{M_{b} }{M_{a} } }[/tex]
[tex]r_{a}[/tex] = Rate of effusion of gas A
[tex]r_{b}[/tex] = Rate of effusion of gas B
[tex]M_{a}[/tex] = Molar mass of gas A
[tex]M_{b}[/tex] = Molar mass of gas B
We are given that, Gas A effuses 0.68 times as fast as Gas B. This means:
[tex]r_{a}[/tex] = 0.68 x [tex]r_{b}[/tex]
Using these values in the formula of Graham's law, we get:
[tex]\frac{0.68\times r_{b} }{r_{b} }=\sqrt{\frac{17}{M_{a} } }\\\\ 0.68=\sqrt{\frac{17}{M_{a} } }\\\\0.68^{2}=\frac{17}{M_{a} }\\\\ M_{a}=\frac{17}{0.68^{2} }=37[/tex]
Therefore, mass of gas A is 37 g, rounded to nearest unit.
