Calculate the ph of a 0.20 m solution of kcn at 25.0 ∘c. express the ph numerically using two decimal places

The pH of a 0.20 M solution of KCN is [tex]\boxed{11.31}[/tex].

Further Explanation:

pH is used to describe acidity or basicity of substances. Its range varies from 0 to 14. It is defined as negative logarithmof hydrogen ion concentration.

The expression for pH is mentioned below.

[tex]{\text{pH}} = - \log \left[ {{{\text{H}}^ + }} \right][/tex]                                                                     …… (1)

Where [tex]\left[ {{{\text{H}}^ + }}\right][/tex] is the concentration of hydrogen ion.

Dissociation reaction of KCN is as follows:

[tex]{\text{KCN}} \to {{\text{K}}^ + } + {\text{C}}{{\text{N}}^ - }[/tex]  

Cyanide ions thus formed can react with water to form HCN and [tex]{\text{O}}{{\text{H}}^ - }[/tex] as follows:

[tex]{\text{C}}{{\text{N}}^ - } + {{\text{H}}_{\text{2}}}{\text{O}} \rightleftharpoons {\text{HCN}} + {\text{O}}{{\text{H}}^ - }[/tex]  

The relation between [tex]{{\text{K}}_{\text{w}}}[/tex], [tex]{{\text{K}}_{\text{b}}}[/tex] and [tex]{{\text{K}}_{\text{a}}}[/tex] is expressed by following relation:

[tex]{{\text{K}}_{\text{w}}} = {{\text{K}}_{\text{b}}} \cdot {{\text{K}}_{\text{a}}}[/tex]                                                                                 …… (2)

Where,

[tex]{{\text{K}}_{\text{w}}}[/tex] is the ionic product constant of water.

[tex]{{\text{K}}_{\text{b}}}[/tex] is the dissociation constant of base.

[tex]{{\text{K}}_{\text{a}}}[/tex] is the dissociation constant of acid.

The value of [tex]{{\text{K}}_{\text{w}}}[/tex] is [tex]{10^{ - 14}}[/tex].

The value of [tex]{{\text{K}}_{\text{a}}}[/tex] is [tex]4.9 \times {10^{ - 10}}[/tex].

Substitute these values in equation (2).

[tex]{10^{ - 14}} = {{\text{K}}_{\text{b}}}\left( {4.9 \times {{10}^{ - 10}}} \right)[/tex]  

Solve for [tex]{{\text{K}}_{\text{b}}}[/tex],

[tex]{{\text{K}}_{\text{b}}} = 2 \times {10^{ - 5}}[/tex]  

The expression for [tex]{{\text{K}}_{\text{b}}}[/tex] of HCN is as follows:

[tex]{{\text{K}}_{\text{b}}} = \dfrac{{\left[ {{\text{HCN}}} \right]\left[ {{\text{O}}{{\text{H}}^ - }} \right]}}{{\left[ {{\text{C}}{{\text{N}}^ - }} \right]}}[/tex]                                                                            …… (3)

Consider x to be change in equilibrium concentration. Therefore, equilibrium concentrationof [tex]{\text{C}}{{\text{N}}^ - }[/tex], HCN and   becomes (0.2 – x), x and x respectively.

[tex]{\text{2}} \times {\text{1}}{{\text{0}}^{ - 5}} = \dfrac{{{x^2}}}{{\left( {0.2 - x} \right)}}[/tex]  

Solving for x,

[tex]x = 0.002[/tex]  

Therefore concentration of hydroxide ion is 0.002 M.

The expression to calculate pOH is as follows:

[tex]{\text{pOH}} = - \log \left[ {{\text{O}}{{\text{H}}^ - }} \right][/tex]                                                                             …… (4)

Substitute 0.002 M for [tex]\left[ {{\text{O}}{{\text{H}}^ - }} \right][/tex] in equation (4).

[tex]\begin{aligned}{\text{pOH}} &= - \log \left( {0.002{\text{ M}}} \right) \\&= 2.69 \\\end{aligned}[/tex]  

The relation between pH and pOH is as follows:

pH + pOH = 14                                                                          …… (5)

Substitute 2.69 for pOH in equation (4).

[tex]{\text{pH}} + 2.69 = 14[/tex]  

Solving for pH,

pH = 11.31

Learn more:

Answer details:

Grade: High School

Subject: Chemistry

Chapter: Acids, base and salts

Keywords: pH, pOH, 11.31, 2.69, 14, 0.002 M, Kb, Kw, Ka, 10^-14, 2*10^-5.

The most probable mechanism of reactivity for the solvolysis of 2-chloro-norbornane is

An archeological artifact was subjected to radiocarbon dating. the artifact showed a carbon-14 decay rate of 13.8 disintegrations/min per gram of carbon. carbon-14 has a half-life of 5715 years, and currently living organisms decay at the rate of 15.3 disintegrations/min per gram of carbon. what is the approximate age of the artifact?

The element that has a valence configuration of 2s2 is ________.

Given the formula m1v1=m2v2, where m indicates concentration and v indicates volume, which equation represents the correct way to find the concentration of the dilute solution (m2)?