Question

What concentration of acetic acid is needed to give a hydrogen ion concentration of $3.5\times 10^{-4}M$ ? $(K_a=1.8\times$ $10^{-5})$

• A. $6.80\times 10^{-3}M$
• B. $3.5\times 10^{-4}M$
• C. $4.2\times 10^{-4}M$
• D. $7.2\times 10^{-4}M$

Answer 1

Answer: (A)

$\underset{C-C\alpha }{C{H}_{3}COOH}\rightleftharpoons \underset{C\alpha }{C{H}_{3}CO{O}^{-}}+\underset{C\alpha }{H^{+}}$ Let the concentration of acetic acid be 'C'.

$K_a=1.8\times 10^{-5}=\frac{C\alpha \cdot C\alpha }{C(1-\alpha )}=C{\alpha }^2$

Now ${\alpha }^2=\frac{K_a}{C}$ or $\alpha =\sqrt{\frac{K_a}{C}}$ or $C\alpha =\sqrt{K_a.C}$

$C\alpha =\left[H^{+}\right]=3.5\times 10^{-4}M$

$\therefore 3.5\times 10^{-4}=\sqrt{1.8\times 10^{-5}C}$

Or $\sqrt{C}=\frac{3.5\times 10^{-4}}{\sqrt{1.8\times 10^{-5}}}$ or $C=\frac{{\left(3.5\times 10^{-4}\right)}^2}{1.8\times 10^{-5}}$

$=\frac{12.25\times 10^{-8}}{1.8\times 10^{-5}}=6.80\times 10^{-3}$