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Question

The pH of $$0.05M$$ aqueous solution of diethylamine is $$12$$. Calculate its $${K}_{b}$$.


Solution

We know that, $$pH+pOH=14$$
or $$pOH=14-pH=14-12-2$$
So, $$\left[ { OH }^{ - } \right] ={ 10 }^{ -2 }$$
$${ \left( { C }_{ 2 }{ H }_{ 5 } \right)  }_{ 2 }NH+{ H }_{ 2 }O\rightleftharpoons { \left( { C }_{ 2 }{ H }_{ 5 } \right)  }_{ 2 }{ NH }_{ 2 }^{ + }+{ OH }^{ - }$$
At equilibrium,$$[{(C_2H_5)}_2NH]=0.05-x,[{(C_2H_5)}_2{NH_2}^+]=x,[OH^-]=x$$
where $$x=0.01mol$$

$${ K }_{ b }=\cfrac { \left[ { \left( { C }_{ 2 }{ H }_{ 5 } \right)  }_{ 2 }{ NH }_{ 2 }^{ + } \right] \left[ { OH }^{ - } \right]  }{ \left[ { \left( { C }_{ 2 }{ H }_{ 5 } \right)  }_{ 2 }NH \right]  } =\cfrac { 0.01\times 0.01 }{ 0.05-0.01 } =\cfrac { 0.01 }{ 4 } =2.5\times { 10 }^{ -3 }$$

Chemistry

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