A certain weak base has a K, of 7.20 × 10-7. What concentration of this base will produce a pH of 10.14?concentration:

Given Kb = 7.20 x 10-7 pH = 10.14 we know pH + pOH = 14 pOH = 14 - 10.14 = 3.86 and [OH-] =…

Answered: A certain weak base has a K, of 7.20 ×…

Chemistry: The Molecular Science

5th Edition

ISBN:9781285199047

Author:John W. Moore, Conrad L. Stanitski

Publisher:John W. Moore, Conrad L. Stanitski

Chapter14: Acids And Bases

Section: Chapter Questions

Problem 32QRT

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A certain weak base has a K, of 7.20 × 10-7. What concentration of this base will produce a pH of 10.14?
concentration:

Expert Solution

Step 1

Given

K_b = 7.20 x 10^-7
pH = 10.14

we know

pH + pOH = 14

pOH = 14 - 10.14 = 3.86

and [OH^-] = 10^-pOH

[OH^-] = 10^-3.86 = 1.5 x 10^-⁴ M

Let the weak base be B .

The balanced chemical reaction is -

B(aq) + H₂O(l) $⇌$ BH⁺(aq) + OH^-(aq)

The equilibrium constant expression is given by -

$K_{b} = \frac{[{BH}^{+}] [{OH}^{-}]}{[B]}$ ------------(1)

[BH⁺] = [OH^-] = 1.5 x 10^-4 M

Substitute all the known values in the equation (1),

$\begin{array}{rcl} 7.20 \times 10^{- 7} & = & \frac{{(1.5 \times 10^{- 4})}^{2}}{[B]} \\ [B] & = & \frac{{(1.5 \times 10^{- 4})}^{2}}{7.20 \times 10^{- 7}} \\ [B] & = & \frac{2.25 \times 10^{- 8}}{7.20 \times 10^{- 7}} \\ [B] & = & 0.03125 M \end{array}$

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