Chemistry - Ideal Gas Question with Solution | TestHub

Each stroke removes $3/4$ of the air, and fresh CO-free air restores the pressure. Therefore, the CO mole fraction is multiplied by $1/4$ per stroke. The concentration after $n$ strokes, $c_n$, can be expressed as:

$$c_n=8.0\%\times {\left(\frac{1}{4}\right)}^n$$

For a safe condition, the CO concentration must be less than $0.0005\%$.

$$8.0\times {\left(\frac{1}{4}\right)}^n<0.0005$$

This inequality can be rewritten as:

$$4^n>\frac{8.0}{0.0005}$$

$$4^n>16000$$

To find the minimum number of strokes, $n$, we evaluate powers of 4:

$4^6=4096$

$4^7=16384$

Since $4^6=4096<16000$ and $4^7=16384>16000$, he needs $n=7$ strokes. After 7 strokes, the concentration $c$ will be:

$$c=\frac{8}{16384}=4.88\times 10^{-4}\%<0.0005\%$$