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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

Although $KOH, RbOH$ and CsOHhave little association between metal and hydroxide in aqueous solution, ${Li}^{+}$ and ${Na}^{+}$ do form complexes with:

role="math" localid="1663390733265" ${Li}^{+} + {OH}^{-} 鈬� LiOH (aq) K_{1} = \frac{[LiOH (aq)]}{[{Li}^{+}] [{OH}^{-}]} = 0.83$

${Na}^{+} + {OH}^{-} 鈬� NaOH (aq) K_{1} = 0.20$

Prepare a table like the one in Exercise 6-B showing initial and final Concentrations of ${Na}^{+} + {OH}^{-} 鈬� NaOH (aq)$ and (aq)insolution. Calculate the fraction of sodium in the form (aq)at equilibrium.

(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.

What concentration of $Fe {(CN)}_{6}^{4 -}$ (ferrocyanide) is in equilibrium with $1.0 渭 M A g^{+}$ androle="math" localid="1663331502441" $A g_{4} F e {(C N)}_{6} (s)$ ? Express your answer with a prefix from Table 1-3.

Calculate the pHof pure water at (a) $25 掳 C$ and (b) $100 掳 C$ .

For the reaction ${HCO}_{3}^{-} 鈬� H^{+} + " {CO}_{3}^{2 -}$ , $螖骋掳 = + 59.0 kJ / mol$ at $298.15 K$ . Find the value of Kfor the reaction.

See all solutions

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