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Chapter 18: Q18.20P (page 824)

What is the difference between $K_{c}$ and $K_{w}$ for the autoionization of water?

Short Answer

Expert verified

The difference is:

$K_{c} = \frac{[H_{3} O^{+}] [{OH}^{-}]}{{[H_{2} O]}^{2}} and K_{w} = [H_{3} O^{+}] [{OH}^{-}]$

Step by step solution

01

Definition of concept

The autoionization of water refers to the reaction of water molecules to form two ions, the hydronium ion, which is $H 3 O^{+}$ , and the hydroxide ion, which is ${OH}^{-}$ .

02

Explanation

The equilibrium constant of water is $K c$

$H_{2} O + H_{2} O 鈬� H_{3} O^{+} + {OH}^{-} K_{c} = \frac{[H_{3} O^{+}] [O H^{-}]}{{[H_{2} O]}^{2}}$

We move it to the other side since the concentration $H_{2} O$ is constant.

$K_{c} {[H_{2} O]}^{2} = [H_{3} O^{+}] [O H^{-}]$

After that, we create a new variable called $K_{c} {[H_{2} O]}^{2}$ , which is the $K_{w}$ . So there you have it.

$K_{w} = K_{c} {[H_{2} O]}^{2} = [H_{3} O^{+}] [O H^{-}]$

Therefore, The difference between $K_{c}$ and $K_{w}$ is that $K_{c} [H_{3} O^{+}]$

$K_{c} = \frac{[H_{3} O^{+}] [{OH}^{-}]}{{[H_{2} O]}^{2}}$ and $K_{w} = [H_{3} O^{+}] [{OH}^{-}]$

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Most popular questions from this chapter

Which of the following are Arrhenius bases?

(a) $H_{3} {AsO}_{4}$

(b) $Ba {(OH)}_{2}$

(c) $HCIO$

(d) $KOH$

Why are most anions basic in $H_{2} O$ ? Give formulas of four anions that are not basic.

Human urine has a normal pH of 6.2. If a person eliminates an average of 1250mL of urine per day, how many $H^{+}$ ions are eliminated per week?

The beakers shown contain 0.300 Lof aqueous solutions of a moderately weak acid HY. Each particle represents 0.010 mol; solvent molecules are omitted for clarity.

(a) The reaction in beaker Ais at equilibrium. Calculate Q for B, C, and D to determine which, if any, is also at equilibrium.

(b) For any not at equilibrium, in which direction does the reaction proceed?

(c) Does dilution affect the extent of dissociation of a weak acid? Explain.

(a) What is the phof ${0.0333 M HNO}_{3}$ ? Is the solution neutral, acidic, or basic?

(b) What is the pOHof $0.0347 M KOH$ ? Is the solution neutral, acidic, or basic?

See all solutions

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