Answer
Verified
408.6k+ views
Hint: Inthe above question is based upon indicator theory. We have to calculate the pH for both the colour range separately using the formula of pH of indicators hence we will get the range in which an indicator will work.
Formula used:
\[{\text{pH = p}}{{\text{K}}_{{{\text{I}}_{\text{n}}}}} + \log \dfrac{{\left[ {{\text{I}}_{\text{n}}^ - } \right]}}{{\left[ {{\text{H}}{{\text{I}}_{\text{n}}}} \right]}}\]
Where p is a operator that represent \[ - {\text{log}}\], \[{{\text{K}}_{{{\text{I}}_{\text{n}}}}}\] is ionization constant, \[\left[ {{\text{I}}_{\text{n}}^ - } \right],\left[ {{\text{H}}{{\text{I}}_{\text{n}}}} \right]\] are concentration of the respective species.
Complete step by step answer:
The ionization of indicator will be as follow:
\[{\text{HIn}} \rightleftharpoons {{\text{H}}^ + } + {{\text{I}}_{\text{n}}}^ - \]
Let us calculate the pH when the solution has yellow colour, that is it is in acidic solution, the ionization constant is given to us and the ratio of yellow form to red form or acid form to base form is given that is 30 to 1. Here \[{\text{HIn}}\] will act as acid form and \[{{\text{I}}_{\text{n}}}^ - \] is basic form so \[\dfrac{{{\text{HIn}}}}{{{{\text{I}}_{\text{n}}}^ - }} = \dfrac{{30}}{1}\] or we can reverse the equation \[\dfrac{{{{\text{I}}_{\text{n}}}^ - }}{{{\text{HIn}}}} = \dfrac{1}{{30}}\]. Substituting the values we will get the value of pH in acidic form
\[{\text{pH = }} - {\text{log(9}} \times {\text{1}}{{\text{0}}^{ - 9}}) + \log \dfrac{2}{1}\]
Solving the above equation we will get, \[{\text{pH = 6}}{\text{.568}}\]
Now we will calculate the pH when the solution has red colour, that is it is in the basic solution, the ionization constant is given to us and the ratio of red form to yellow form or base form to acid form is given that is 30 to 1. Here \[{\text{HIn}}\] will act as basic form and \[{{\text{I}}_{\text{n}}}^ - \] is acid form because indicator is in basic solution. So \[\dfrac{{{\text{HIn}}}}{{{{\text{I}}_{\text{n}}}^ - }} = \dfrac{2}{1}\] . Substituting the values we will get the value of pH in acidic form
\[{\text{pH = - log(9}} \times {\text{1}}{{\text{0}}^{ - 9}}) + \log \dfrac{2}{1}\]
Solving the above equation we will get, \[{\text{pH = 8}}{\text{.346}}\].
Hence the range of the indicator will be \[6.568{\text{ to 8}}{\text{.346}}\] , i.e. Option B.
Note:
Indicators are weak organic acid or weak organic bases, which show different colours in ionized and unionized form. The intensity of colour will depend upon the concentration of colour imparting species. The two colour imparting species are: \[{\text{HIn}}\] and \[{{\text{I}}_{\text{n}}}^ - \].
Formula used:
\[{\text{pH = p}}{{\text{K}}_{{{\text{I}}_{\text{n}}}}} + \log \dfrac{{\left[ {{\text{I}}_{\text{n}}^ - } \right]}}{{\left[ {{\text{H}}{{\text{I}}_{\text{n}}}} \right]}}\]
Where p is a operator that represent \[ - {\text{log}}\], \[{{\text{K}}_{{{\text{I}}_{\text{n}}}}}\] is ionization constant, \[\left[ {{\text{I}}_{\text{n}}^ - } \right],\left[ {{\text{H}}{{\text{I}}_{\text{n}}}} \right]\] are concentration of the respective species.
Complete step by step answer:
The ionization of indicator will be as follow:
\[{\text{HIn}} \rightleftharpoons {{\text{H}}^ + } + {{\text{I}}_{\text{n}}}^ - \]
Let us calculate the pH when the solution has yellow colour, that is it is in acidic solution, the ionization constant is given to us and the ratio of yellow form to red form or acid form to base form is given that is 30 to 1. Here \[{\text{HIn}}\] will act as acid form and \[{{\text{I}}_{\text{n}}}^ - \] is basic form so \[\dfrac{{{\text{HIn}}}}{{{{\text{I}}_{\text{n}}}^ - }} = \dfrac{{30}}{1}\] or we can reverse the equation \[\dfrac{{{{\text{I}}_{\text{n}}}^ - }}{{{\text{HIn}}}} = \dfrac{1}{{30}}\]. Substituting the values we will get the value of pH in acidic form
\[{\text{pH = }} - {\text{log(9}} \times {\text{1}}{{\text{0}}^{ - 9}}) + \log \dfrac{2}{1}\]
Solving the above equation we will get, \[{\text{pH = 6}}{\text{.568}}\]
Now we will calculate the pH when the solution has red colour, that is it is in the basic solution, the ionization constant is given to us and the ratio of red form to yellow form or base form to acid form is given that is 30 to 1. Here \[{\text{HIn}}\] will act as basic form and \[{{\text{I}}_{\text{n}}}^ - \] is acid form because indicator is in basic solution. So \[\dfrac{{{\text{HIn}}}}{{{{\text{I}}_{\text{n}}}^ - }} = \dfrac{2}{1}\] . Substituting the values we will get the value of pH in acidic form
\[{\text{pH = - log(9}} \times {\text{1}}{{\text{0}}^{ - 9}}) + \log \dfrac{2}{1}\]
Solving the above equation we will get, \[{\text{pH = 8}}{\text{.346}}\].
Hence the range of the indicator will be \[6.568{\text{ to 8}}{\text{.346}}\] , i.e. Option B.
Note:
Indicators are weak organic acid or weak organic bases, which show different colours in ionized and unionized form. The intensity of colour will depend upon the concentration of colour imparting species. The two colour imparting species are: \[{\text{HIn}}\] and \[{{\text{I}}_{\text{n}}}^ - \].
Recently Updated Pages
In a flask the weight ratio of CH4g and SO2g at 298 class 11 chemistry CBSE
In a flask colourless N2O4 is in equilibrium with brown class 11 chemistry CBSE
In a first order reaction the concentration of the class 11 chemistry CBSE
In a first order reaction the concentration of the class 11 chemistry CBSE
In a fermentation tank molasses solution is mixed with class 11 chemistry CBSE
In a face centred cubic unit cell what is the volume class 11 chemistry CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
Name 10 Living and Non living things class 9 biology CBSE
Black foot disease is caused by the pollution of groundwater class 12 biology CBSE