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Chapter 14: Q14.3-35 E (page 829)

What is the ionization constant at 25oC for the weak acid \(C{H_3}NH_3^ + \), the conjugate acid of the weak base \(C{H_3}N{H_2}\)\({K_b} = 4.4 \times 1{0^{ - 4}}\) ,.

Short Answer

Expert verified

Ionization constant for weak acid is

\({K_a} = 2.3 \times 1{0^{ - 11}}\)

Step by step solution

01

Given Information

For weak acid and the weak base,\({K_b} = 4.4 \times 1{0^{ - 4}}\)

02

Calculating ionization constant of an acid

Given weak conjugated acid as\(C{H_3}NH_3^ + \)

\(C{H_3}NH_3^ + (aq) + {H_2}O(l) \to C{H_3}N{H_2}(aq) + {H_3}{O^ + }(aq)\)

To calculate Ionization equation

\({K_a} = \frac{{c\left( {C{H_3}N{H_2}} \right) \times c\left( {{H_3}{O^ + }} \right)}}{{c\left( {C{H_3}NH_3^ + } \right)}}\)

Ionization constant of a weak base \(C{H_3}N{H_2}\)Dissociation equation is

\(C{H_3}N{H_2}(aq) + {H_2}O(l) \to C{H_3}NH_3^ + (aq) + O{H^ - }(aq)\)

Ionization constant is

\({K_b} = \frac{{c\left( {C{H_3}NH_3^ + } \right) \times c\left( {O{H^ - }} \right)}}{{c\left( {C{H_3}N{H_2}} \right)}}\)

\({K_b} = 4.4 \times 1{0^{ - 4}}\)

Equation for dissociation for water is

\({H_2}O(l) + {H_2}O(l) \to {H_3}{O^ + }(aq) + O{H^ - }(aq)\)

Constant of water ionization for \({K_w}\)is

\({K_w} = c\left( {{H_3}{O^ + }} \right) \times c\left( {O{H^ - }} \right)\)

\({K_w} = 1.0 \times 1{0^{ - 14}}\)

Concentration of \(C{H_3}N{H_2}\)is

\({K_b} = \frac{{c\left( {C{H_3}NH_3^ + } \right) \times c\left( {O{H^ - }} \right)}}{{c\left( {C{H_3}N{H_2}} \right)}}\)

\({K_b} \times c\left( {c{H_3}N{H_2}} \right) = c\left( {C{H_3}NH_3^ + } \right) \times c\left( {O{H^ - }} \right)\)

\(c\left( {C{H_3}N{H_2}} \right) = \frac{{c\left( {C{H_3}NH_3^ + } \right) \times c\left( {O{H^ - }} \right)}}{{{K_b}}}\)

\({K_a} = \frac{{c\left( {C{H_3}N{H_2}} \right) \times c\left( {{H_3}{O^ + }} \right)}}{{c\left( {C{H_3}NH_3^ + } \right)}}\)

\({K_a} = \frac{{c\left( {C{H_3}NH_3^ + } \right) \times c\left( {O{H^ - }} \right) \times c\left( {{H_3}{O^ + }} \right)}}{{c\left( {C{H_3}NH_3^ + } \right) \times {K_b}}}\)

Concentration of \(C{H_3}NH_3^ + \)each other, we get

\({K_a} = \frac{{c\left( {O{H^ - }} \right) \times c\left( {{H_3}{O^ + }} \right)}}{{{K_b}}}\)

Replacing \(c\left( {O{H^ - }} \right) \times c\left( {{H_3}{O^ + }} \right)\) as \({K_w}\)

\({K_a} = \frac{{{K_w}}}{{{K_b}}}\)

Ionization of a weak acid is

\({K_a} = \frac{{1.0 \times 1{0^{ - 14}}}}{{4.4 \times 1{0^{ - 4}}}}\)

\({K_a} = 2.3 \times 1{0^{ - 11}}\)

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Most popular questions from this chapter

What is the effect on the concentration of ammonia, hydroxide ion, and ammonium ion when the following are added to a basic buffer solution of equal concentrations of ammonia and ammonium nitrate:

(a)\(KI\)

(b)\(N{H_3}\)

(c)\(HI\)

(d)\(NaOH\)

(e)\(N{H_4}Cl\)

We can ignore the contribution of water to the concentration of\(O{H^ - }\)in a solution of the following bases:\(0.0784 M {C_6}{H_5}N{H_2}\), a weak base\(0.11M{\left( {C{H_3}} \right)_3}\;N\), a weak base but not the contribution of water to the concentration of\({H_3}{O^ + }?\)

The ionization constant for water\(\left( {{K_w}} \right)\;is\;9.311 \times 1{0^{ - 14}}\;at\;6{0^o}C\). Calculate \(\left( {{H_3}{O^ + }} \right),\left( {O{H^ - }} \right),pH,\;and\;pOH\)for pure water at \(6{0^o}C\).

Identify and label the Brønsted-Lowry acid, its conjugate base, the Brønsted-Lowry base, and its conjugate acid in each of the following equations:

\({\rm{\;(a)\;HN}}{{\rm{O}}_3} + {{\rm{H}}_2}{\rm{O}} \to {{\rm{H}}_3}{{\rm{O}}^ + } + {\rm{NO}}_3^ - \)

\({\rm{b) C}}{{\rm{N}}^ - } + {{\rm{H}}_2}{\rm{O}} \to {\rm{HCN}} + {\rm{O}}{{\rm{H}}^ - }\)

\({\rm{\;(c)\;}}{{\rm{H}}_2}{\rm{S}}{{\rm{O}}_4} + {\rm{C}}{{\rm{l}}^ - } \to {\rm{HCl}} + {\rm{HSO}}_4^ - \)

\({\rm{\;(d)\;HSO}}_4^ - + {\rm{O}}{{\rm{H}}^ - } \to {\rm{SO}}_4^{2 - } + {{\rm{H}}_2}{\rm{O}}\)

\({\rm{\;(e)\;}}{{\rm{O}}^{2 - }} + {{\rm{H}}_2}{\rm{O}} \to 2{\rm{O}}{{\rm{H}}^ - }\)

\({\rm{\;(f)\;}}{\left( {{\rm{Cu}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_3}({\rm{OH}})} \right)^ + } + {\left( {{\rm{Al}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_6}} \right)^{3 + }} \to {\left( {{\rm{Cu}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_4}} \right)^{2 + }} + {\left( {{\rm{Al}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_5}({\rm{OH}})} \right)^{2 + }}\)

\({\rm{\;(g)\;}}{{\rm{H}}_2}{\rm{S}} + {\rm{NH}}_2^ - \to {\rm{H}}{{\rm{S}}^ - } + {\rm{N}}{{\rm{H}}_3}\)

Is the self ionization of water endothermic or exothermic? The ionization constant for water \(\left( {{K_W}} \right)\)is 2.9* \({10^{ - 14}}\)at \({40^ \circ }{\rm{C}}\)and 9.3 x \({10^{ - 14}}\)at \({60^ \circ }{\rm{C}}\)
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