Chapter 9: Q25P (page 209)

Show that the limiting fraction of association of a base in water, as the concentration of base approaches $0, is a = 10^{7} Kb / (1 + 10^{7} K_{b})$ Find the limiting value of $a$ for $K_{b} = 10^{- 4}$ and for $K_{b} = 10^{- 10}$

Short Answer

Expert verified

The $limiting value of α for K_{b} = 10^{- 4} and for K_{b} = 10^{- 10}$ is 0.999 and 0.000999 respectively.

Step by step solution

Showing statement is true.

When bases approaches , $pH = 7 and [{OH}^{-}] = 10^{- 7} M$

$K_{b} = \frac{[{BH}^{+}] [{OH}^{-}]}{[B]} = \frac{[{BH}^{+}]}{[B] \times 10^{- 7}} [{BH}^{+}] = 10^{7} K_{b} [B]$

Showing that the statement is true:

$α = \frac{[{BH}^{+}]}{[B] + [{BH}^{+}]} = \frac{10^{7} K_{b} [B]}{[B] + 10^{7} K_{b} [B]} = 10^{7} K_{b} / (1 + 10^{7} K_{b})$

Finding limiting value α for Kb=10-4and for Kb=10-10:

$a) for K_{b} = 10^{- 4} α = 10^{7} K_{b} / (1 + 10^{7} K_{b}) = 10^{7} \times 10^{- 4} / (1 + 10^{7} \times 10^{- 4}) = 0.999 b) for K_{b} = 10^{- 10} α = 10^{7} K_{b} / (1 + 10^{7} K_{b}) = 10^{7} \times 10^{(} - 10) / (1 + 10^{7} \times 10^{- 10}) = 0.000999$

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Show that the limiting fraction of association of a base in water, as the concentration of base approaches $0, is a = 10^{7} Kb / (1 + 10^{7} K_{b})$ Find the limiting value of $a$ for $K_{b} = 10^{- 4}$ and for $K_{b} = 10^{- 10}$

Short Answer

Step by step solution

Showing statement is true.

Finding limiting value α for Kb=10-4and for Kb=10-10:

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Show that the limiting fraction of association of a base in water, as the concentration of base approaches0,isa=107Kb/(1+107Kb)Find the limiting value ofaforKb=10-4and forKb=10-10

Short Answer

Step by step solution

Showing statement is true.

Finding limiting value α for Kb=10-4and for Kb=10-10:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Making Measurements

Physical Chemistry

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Nuclear Chemistry

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Study anywhere. Anytime. Across all devices.

Show that the limiting fraction of association of a base in water, as the concentration of base approaches $0, is a = 10^{7} Kb / (1 + 10^{7} K_{b})$ Find the limiting value of $a$ for $K_{b} = 10^{- 4}$ and for $K_{b} = 10^{- 10}$