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never [62]
3 years ago
7

Calculate the solubility of mn(oh)2 in grams per liter when buffered at ph=7.0. assume that buffer capacity is not exhausted

Chemistry
2 answers:
Gwar [14]3 years ago
6 0

The solubility of {\text{Mn}}{\left( {{\text{OH}}} \right)_2} in grams per litre is \boxed{0.002001{\text{ g/L}}}.

Further explanation:

Solubility product constant:

It is the equilibrium constant for the reaction that comes into play when an ionic compound is dissolved to produce its respective ions. It is represented by {{\text{K}}_{{\text{sp}}}}. Consider {{\text{A}}_x}{{\text{B}}_y} to be an ionic compound. Its dissociation occurs as follows:

 {{\text{A}}_x}{{\text{B}}_y} \rightleftharpoons x{{\text{A}}^{y + }} + y{{\text{A}}^{x - }}

The expression for its {{\text{K}}_{{\text{sp}}}} is as follows:

 {{\text{K}}_{{\text{sp}}}} = {\left[ {{{\text{A}}^{y + }}} \right]^x}{\left[ {{{\text{B}}^{x - }}} \right]^y}

Here,

{{\text{K}}_{{\text{sp}}}} is the solubility product constant.

\left[ {{{\text{A}}^ + }} \right] is the concentration of  ions.

\left[ {{{\text{B}}^ - }} \right] is the concentration of  ions.

The relation between pH and pOH of the solution is given by the following formula:

{\text{pH}} + {\text{pOH}} = {\text{14}}   ...... (1)                                                                

Rearrange equation (1) to calculate the pOH of the solution.

{\text{pOH}} = {\text{14}} - {\text{pH}}  ...... (2)                                                                  

The value of pH is 7. Substitute this value in equation (2).

 \begin{aligned}{\text{pOH}} &= {\text{14}} - {\text{7}}\\&= {\text{7}}\\\end{aligned}

The expression for pOH is as follows:

{\text{pOH}} =  - \log \left[ {{\text{O}}{{\text{H}}^ - }} \right]  ...... (3)                                                              

Rearrange equation (3) for \left[ {{\text{O}}{{\text{H}}^ - }} \right].

 \left[ {{\text{O}}{{\text{H}}^ - }} \right] = {10^{ - {\text{pOH}}}} ...... (4)                                                                

The value of pOH is 7. Substitute this value in equation (4).

 \left[ {{\text{O}}{{\text{H}}^ - }} \right] = {10^{ - 7}}{\text{ M}}

The dissociation reaction of {\text{Mn}}{\left( {{\text{OH}}} \right)_{\text{2}}} is as follows:

 {\text{Mn}}{\left( {{\text{OH}}} \right)_{\text{2}}}\left( {aq} \right) \rightleftharpoons {\text{M}}{{\text{n}}^{2 + }}\left( {aq} \right) + 2{\text{O}}{{\text{H}}^ - }\left( {aq} \right)

Let us consider the solubility of {\text{Mn}}{\left( {{\text{OH}}} \right)_2} be s. Therefore, after dissociation, the concentration of {\text{M}}{{\text{n}}^{2 + }} and {\text{O}}{{\text{H}}^ - } are s and {10^{ - 7}} + 2s respectively.

The formula to calculate the molar solubility of  is as follows:

{{\text{K}}_{{\text{sp}}}} = \left[ {{\text{M}}{{\text{n}}^{{\text{2 + }}}}}\right]{\left[ {{\text{O}}{{\text{H}}^ - }}\right]^2}  …… (5)                                                                                        

Substitute s for \left[ {{\text{M}}{{\text{n}}^{{\text{2 + }}}}} \right], {10^{ - 7}} + 2s for \left[ {{\text{O}}{{\text{H}}^ - }} \right] and {\text{4}}{\text{.6}} \times {10^{ - 14}} for {{\text{K}}_{{\text{sp}}}} in equation (5).

{\text{4}}{\text{.6}} \times {10^{ - 14}} = \left( s \right){\left( {{{10}^{ - 7}} + 2s} \right)^2}  

Solve for s,

s = 2.25 \times {10^{ - 5}}{\text{ M}}

Therefore the solubility of {\text{Mn}}{\left( {{\text{OH}}} \right)_{\text{2}}} comes out to be 2.25 \times {10^{ - 5}}{\text{ M}}.

The formula to calculate the solubility of {\text{Mn}}{\left( {{\text{OH}}} \right)_{\text{2}}} in g/L is as follows:

\begin{aligned}{\text{Solubility of Mn}}{\left( {{\text{OH}}} \right)_{\text{2}}}\left( {{\text{g/L}}} \right) &= \left( {{\text{Solubility of Mn}{{\left({{\text{OH}}}\right)}_{\text{2}}}\left( {{\text{mol/L}}} \right)} \right)\\\left( {{\text{Molar mass of Mn}}{{\left( {{\text{OH}}} \right)}_{\text{2}}}} \right) \\ \end{aligned}                …… (6)

Substitute 2.25 \times {10^{ - 5}}{\text{ M}} for solubility and 88.95 g/mol in equation (6).

 \begin{aligned}{\text{Solubility of Mn}}{\left( {{\text{OH}}} \right)_{\text{2}}} &= \left( {\frac{{2.25 \times {{10}^{ - 5}}{\text{ mol}}}}{{{\text{1 L}}}}} \right)\left({\frac{{{\text{88}}{\text{.95 g}}}}{{{\text{1 mol}}}}} \right)\\&= 0.002001{\text{ g/L}}\\\end{aligned}

Learn more:

  1. Sort the solubility of gas will increase or decrease: brainly.com/question/2802008.
  2. What is the pressure of the gas? brainly.com/question/6340739.

Answer details:

Grade: School School

Subject: Chemistry

Chapter: Chemical equilibrium

Keywords: solubility, Mn2+, 2OH-, Mn(OH)2, Ksp, solubility product, molar mass, 88.95 g/mol, 0.002001 g/L.

Vanyuwa [196]3 years ago
3 0
When PH + POH = 14 
∴ POH = 14 -7 = 7

when POH = -㏒[OH-]

          7    = -㏒ [OH-]
∴[OH-] = 10^-7

by using ICE table:

           Mn(OH)2(s) ⇄  Mn2+ (aq)  + 2OH-(aq)
initial                              0                     10^-7
change                           +X                      +2X
Equ                                 X                  (10^-7 + 2X)

when Ksp = [Mn2+][OH-]^2

when Ksp of Mn(OH)2 = 4.6 x 10^-14

by substitution:

4.6 x 10^-14 = X*(10^-7+2X)^2  by solving this equation for X

∴ X =2.3 x 10-5 M

∴ The solubility of Mn(OH)2 in grams per liter (when the molar mass of Mn(OH)2 = 88.953 g/mol
= 2.3 x10^-5 moles/L * 88.953 g/mol

= 0.002 g/ L
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