Question

What indicator should be used (in terms of its $p{K}_{in}$)for the titration of 0.10 M $K{H}_{2}B{O}_3$ with 0.10 M $HCl$ ?

• A. pK_in = 2.2
• B. pK_in = 5.22
• C. pK_in = 9.56
• D. pK_in = 6.6

Answer 1

The correct option is B

pK_in = 5.22

$H_{2}B{O}_3^{+}+H_3{O}^{+}\to H_{3}B{O}_3+H_{2}O$

At the equivalence point, 0.050 M $H_{3}B{O}_3$ would be produced.

Only the first ionization step of $H_{3}B{O}_3$ is important to the pH.

$H_{3}B{O}_3+H_{2}O\to H_{2}B{O}_3^{+}+H_3{O}^{+}$

$K_a$= $\frac{\left[H_3{O}^{+}\right]\left[H_{2}B{O}_3^{-}\right]}{\left[H_{3}B{O}_3\right]}$ = $\frac{x^2}{0.050}$

= $7.3\times {10}^{-10}$ thus x = $6.0\times {10}^{-6}$ and pH = 5.22

pH 5.22 is in the middle of the range of methyl red, which would therefore be suitable.