Question

Amphetamine $\left(C_3{H}_{13}N\right)$ is a weak base with $p{K}_b$ of $4.2$. Calculate the $pH$ of a solution containing an amphetamine concentration of $220mg/L$.

• A. $3.49$
• B. $5.21$
• C. $10.5$
• D. $13.7$

Answer 1

The correct option is C $10.5$

Let $B$ represents $C_9{H}_{13}N$. (Molar mass $=135$)

$\left[B\right]=0.001629$ mol/L $(C=\frac{220\times {10}^{-3}}{135}=0.001629)$

$p{K}_b=4.2\Rightarrow K_b={10}^{-4.2}=6.31\times {10}^{-5}$

$B+H_{2}O⟶{BH}^{+}+{OH}^{-}$

$\left[{BH}^{+}\right]=\left[{OH}^{-}\right]=X$

$\left[{OH}^{-}\right]=\sqrt{K_{b}C}=\sqrt{6.31\times {10}^{-5}\times 0.001629}$

$=\sqrt{1.0279\times {10}^{-7}}$

$=0.000320$

$\Rightarrow pOH=3.49$

So $pH=14-3.49=10.50$