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Chapter 6: Q16 P (page 142)

Find $[{Cu}^{2 +}]$ in a solution saturated with ${Cu}_{4} {(OH)}_{6} ({so}_{4})$ if $[{OH}^{-}]$ is fixed at $1.0 脳 10^{- 6} M$ . Note that ${Cu}_{4} {(OH)}_{6} ({so}_{4})$ gives 1mol of ${SO}_{4}^{2 -}$ 4 mol for of ${Cu}^{2 +}$ .
${Cu}_{4} {(OH)}_{6} ({so}_{4}) (s) 鈬� 4 C u^{2 +} + 6 O H^{-} + S O_{4}^{2 -} K_{s p} = 2.3 脳 10^{- 69}$

Short Answer

Expert verified

$[{Cu}^{2 +}]$ was calculated as $3.9 脳 10^{- 7} M$

Step by step solution

01

Definition of solubility product

Solubility product $(K_{sp})$ :

It is defined as the mathematical product of the concentration of the dissolved constituent ions raised up to the power of their stoichiometric coefficient.

$M_{y} X_{z (s)} 鈬� {yM}^{z +} (aq) + {zX}^{y -} (aq) K_{sp} = {[M^{z +}]}^{y} {[X^{y -}]}^{z}$

02

Calculate the concentration of [Cu2+]The dissociation reaction is:

${Cu}_{4} {(OH)}_{6} ({so}_{4}) (s) 鈬� 4 {Cu}^{2 +} + 6 {OH}^{-} + {SO}_{4}^{2 -}$

From the balanced reversible reaction, it is seen that 1 mol ${Cu}_{4} {(OH)}_{6} ({so}_{4})$ of dissociates to give 4 mol ${Cu}^{2 +}$ of and 1 mol of ${SO}_{4}^{2 -}$ .

Lets take $4 x = [{Cu}^{2 +}]$ ; then $X = [{SO}_{4}^{2 -}]$

$K = {[C u^{2 +}]}^{4} {[O H^{-}]}^{6} [S O_{4}^{2 -}] 2.3 脳 10^{- 69} = {(4 x)}^{4} 脳 (1.0 脳 10^{- 6}) 脳 x 2.3 脳 10^{- 69} = x^{5} 脳 (1.0 脳 10^{- 6}) 脳 256$

$x = [C u^{2 +}] = {(\frac{(2.3 脳 10^{- 69})}{256 脳 (1.0 脳 10^{- 6}) 6})}^{\frac{1}{5}} = 3.9 脳 10^{- 7} M$

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Most popular questions from this chapter

(a) From the solubility product of zinc ferrocyanide, ${Zn}_{2} Fe {(CN)}_{6}$ , calculate the concentration of $Fe {(CN)}_{6}^{4 -}$ in 0.1 0m M ${ZnSO}_{4}$ saturated with ${Zn}_{2} Fe {(CN)}_{6}$ . Assume that ${Zn}_{2} Fe {(CN)}_{6}$ is a negligible source of ${Zn}^{2 +}$ .

(b) What concentration of $K_{4} Fe {(CN)}_{6}$ should be in a suspension of solid ${Zn}_{2} Fe {(CN)}_{6}$ in water to give $[{Zn}^{2 +}] = 5.0 脳 10^{- 7} M$ ?

For $H_{2} (g) + B r_{2} (g) 鈬� 2 H B r (g), K = 7.2 脳 10^{- 4}$ at 1362Kand $鈭� H^{掳}$ is positive. A vessel is charged with $48.0 Pa H Br, 1370 Pa H_{2}$ , and $3310 Pa {Br}_{2}$ at1362K.

(a) Will the reaction proceed to the left or the right to reach equilibrium?

(b) Calculate the pressure (Pa) of each species at equilibrium.

(c) If the mixture at equilibrium is compressed to half of its original volume, will the reaction proceed to the left or the right to re-establish equilibrium?

(d) If the mixture at equilibrium is heated from 1362 to 1407K , will HBr be formed or consumed in order to re-establish equilibrium?

Write the autoprotolysis reaction of $H_{2} {SO}_{4}$ .

Identify the conjugate acid-base pairs in the following reactions:

(a) $H_{3} {NCH}_{2} {CH}_{2} {NH}_{3} + H_{2} O 鈬� H_{3} {NCH}_{2} {CH}_{2} {NH}_{2} + H_{3} O^{+}$

(b) Benzoicacid+ Pyridine $鈬�$ Benzoate+ Pyridinium

(a) A favorable entropy change occurs when $鈭� S$ is positive. Does the order of the system increase or decrease when $鈭� S$ is positive?

(b) A favorable enthalpy change occurs when $鈭� H$ is negative. Does the system absorb heat or give off heat when $鈭� H$ is negative?

(c) Write the relation between $鈭� G$ , $鈭� H$ and $鈭� S$ . Use the results of parts (a) and (b) to state whether $鈭� G$ must be positive or negative for a spontaneous change.

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