Question #ba54f

Question

Question #ba54f

1 Answer

Impact of this question

2731 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-24T10:39:12

$\frac{[B]}{[{BH}^{+}]} = 0.0281$ $(["B"])/(["BH"^(+)]) = 0.0281$

Explanation:

There are two ways in which you can approach this problem, one using the base dissociation constant and the solution's $p O H$ $pOH$ , and the other one using the acid dissociation constant and the solution's pH.

I'll show you how to solve it using $K_{b}$ $K_b$ and $[{OH}^{-}]$ $["OH"^(-)]$ , and you try the other approach as practice. So, you know that you're dealing with a weak base that has the base dissociation constant, $K_{b}$ $K_b$ , equal to $8.91 \cdot 10^{- 6}$ $8.91 * 10^(-6)$ .

The equilibrium dissociation of the weak base, which I'll call $B$ $"B"$ for simplicity, looks like this

$B_{(aq]} + H_{2} O_{(l]} ⇌ {BH}_{(aq]}^{+} + {OH}_{(aq]}^{-}$ $"B"_text((aq]) + "H"_2"O"_text((l]) rightleftharpoons "BH"_text((aq])^(+) + "OH"_text((aq])^(-)$

By definition, the base dissciation constant is equal to

$K_{b} = \frac{[{BH}^{+}] \cdot [{OH}^{-}]}{[B]}$ $K_b = (["BH"^(+)] * ["OH"^(-)])/([B])$

Use the blood's pH to determine what the $p O H$ $pOH$ is

$p H_{sol} + p O H = 14 \Rightarrow p O H = 14 - p H_{sol}$ $pH_"sol" + pOH = 14 implies pOH = 14 - pH_"sol"$

$p O H = 14 - 7.4 = 6.6$ $pOH = 14 - 7.4 = 6.6$

The concentration of the hydroxide ions present in solution will be

$[{OH}^{-}] = 10^{- p O H}$ $["OH"^(-)] = 10^(-pOH)$

$[{OH}^{-}] = 10^{- 6.6} = 2.5 \cdot 10^{- 7} M$ $["OH"^(-)] = 10^(-6.6) = 2.5 * 10^(-7)"M"$

Rearrange the equation for $K_{b}$ $K_b$ to get

$K_{b} \cdot [B] = [{BH}^{+}] \cdot [{OH}^{-}]$ $K_b * ["B"] = ["BH"^(+)] * ["OH"^(-)]$

$\frac{[B]}{[{BH}^{+}]} = \frac{[{OH}^{-}]}{K_{b}} = \frac{2.5 \cdot 10^{- 7}}{8.91 \cdot 10^{- 6}} = 0.0281$ $(["B"])/(["BH"^(+)]) = (["OH"^(-)])/K_b = (2.5 * 10^(-7))/(8.91 * 10^(-6)) = color(green)(0.0281)$

Science

Math

Humanities

... and beyond

Question #ba54f

1 Answer

Explanation:

Related questions

Impact of this question