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Chapter 19: Q19.72P (page 875)

The solubility of silver dichromate at $15 掳 C$ is $8.3 脳 10^{- 3} g / 100 mL$ solution. Calculate its $K_{s p}$ .

Short Answer

Expert verified

The $K_{s p}$ of silver dichromate is $2.84 脳 10^{- 11}$ .

Step by step solution

01

Concept Introduction

The chemical substance silver dichromate has the formula ${Ag}_{2} {Cr}_{2} O_{7}$ .

It is water insoluble and decomposes when exposed to hot water.

Its anion has a $- 2$ charge.

02

Constructing the ICE table

To calculate the $K_{sp}$ of silver dichromate, we first need to write the reaction equation of the dissolution of ${Ag}_{2} {Cr}_{2} O_{7}$ .

${Ag}_{2} {Cr}_{2} O_{7} 鈬� 2 {Ag}^{+} + {Cr}_{2} O_{7}^{2 -}$

Write the $K_{sp}$ expression for the reaction.

$K_{sp} = {[{Ag}^{+}]}^{2} [{Cr}_{2} O_{7}^{2 -}]$

Constructing the ICE table,

Now, we need to substitute it for the $K_{s p}$ expression.

$K_{sp} {= [2s]}^{2} [s] K_{sp} {= 4s}^{3}$

Solving for $s$ from the solubility given,

localid="1663315831345" $s = \frac{mol}{L} = \frac{8.3 脳 10^{- 3} g {Ag}_{2} {Cr}_{2} O_{7} 脳 \frac{1 mol {Ag}_{2} {Cr}_{2} O_{7}}{431.76 g {Ag}_{2} {Cr}_{2} O_{7}}}{100 mL 脳 \frac{1 L}{1000 mL}} = 1.92 脳 10^{- 4} .$

03

Calculating the Ksp of silver dichromate

Now solve for $K_{sp}$ ,

$K_{s p} = 4 s^{3} = 4 {(1.92 脳 10^{- 4})}^{3} = 2.84 脳 10^{- 11}$

Therefore, the $K_{s p}$ of silver dichromate is $2.84 脳 10^{- 11}$ .

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Most popular questions from this chapter

Find the pH of a buffer that consists of 0.12M boric acid ( $H_{3} {BO}_{3}$ ) and 0.82M sodium borate( ${NaH}_{2} {BO}_{3}$ ) ( ${pK}_{a}$ of boric acid=9.24)?

A buffer consists of 0.50M ${NaH}_{2} {PO}_{4}$ and 0.40M ${Na}_{2} {HPO}_{4}$ . Phosphoric acid is a triprotic acid ( $K_{a1} {= 7.2脳10}^{- 3} {,K}_{a2} {= 6.3脳10}^{- 8}$ and $K_{a3} {= 4.2脳10}^{- 1}$ ).

(a) Which $K_{a}$ value is most important to this buffer?

(b) What is the buffer pH?

Which compound in each pair is more soluble in water?

(a) Magnesium hydroxide or nickel (II)hydroxide

(b) Lead (II)sulphide or copper (II)sulphide

(c) Silver sulphate or magnesium fluoride

A buffer that contains $0.40 M$ base, B, and $0.25 M$ of its conjugate acid, ${BH}^{+}$ , has a pHof $8.88$ . What is the pHafter $0.0020$ mol of HCLis added to $0.25 L$ of this solution?

Write the ion-product expressions for

$(a) calcium chromate; (b) silver cyanide; (c) nickel (II) sulfide$

See all solutions

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