Question

For an elementary reaction, $X\left(g\right)\to Y\left(g\right)+Z\left(g\right)$
the half life period is $10$ min. In what period of time would concentration of $X$ be reduced to $10$% of original concentration?

• A. $20$ Min
• B. $33$ Min.
• C. $15$ Min
• D. $25$ Min

Answer 1

The correct option is B $33$ Min.

Given, $t_{\frac{1}{2}}=10min$

For elementary reaction $X_{\left(g\right)}⟶Y_{\left(g\right)}+Z_{\left(g\right)}$

$A=A_0{e}^{-kt}⟶\left(i\right)$ Where $A_0$ is initial concentration, while $A$ concentration at time $t.$

Since, $K=\frac{0.693}{t_{112}}=\frac{0.693}{10}=0.0693$

From equation $\left(i\right)$, we have

$0.1A_0=A_0{e}^{-0.0693\times t}$

In $0.1=-0.0693\times t$

$-2.303=-0.0693t$

$t=33.23min.\approx 33min$