Question

$100ml$ of $O_2$ gas diffuses in $10$ seconds. $100ml$ of gas $x$ diffuses in $t$ seconds. Gas $x$ and time $t$ can be respectively:

• A. $H_2,2.5$ seconds
• B. ${SO}_2$, $16$ seconds
• C. $CO$,$10$ seconds
• D. $He$, $4$ seconds

Answer 1

The correct option is A $H_2,2.5$ seconds

If the volume of both the gases are same then,

$\frac{t_2}{t_1}=\sqrt{\frac{M_2}{M_1}}$

GIven :

$t_1=10s$

$M_1=32g$

$t_2=t$

$M_2=M$

Now, $\frac{t}{10}=\sqrt{\frac{M}{32}}$

Since two unknowns are present we can substitute the values from the given options and then find the right answer.

For $M=2t=2.5sec$

$\frac{2.5}{10}=\sqrt{\frac{2}{32}}$

$\frac{1}{4}=\sqrt{\frac{1}{16}}$

$\frac{1}{4}=\frac{1}{4}$

LHS=RHS

Hence, Gas x is $H_2$ and time t is $2.5seconds$