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As per the Ostwalds Theory, Indicators are weak organic acids or bases. These indicators undergo ionization reaction when dissolved in water as follows,
For Acidic Indicator $$(H-In) H-In + { H }_{ 2 }O \rightleftharpoons { H }_{ 3 }{ O }^{ + } + { In }^{ - }\qquad ....(1)$$ For Basic Indicator $$(In-OH) In-OH \overset { { H }_{ 2 }O }{ \rightleftharpoons } { OH }^{ - } + { In }^{ + }\qquad ....(2)$$ On applying law of mass action for acidic reaction,$$ { K }_{ In } = \frac { \left[ { H }_{ 3 }{ O }^{ + } \right] \left[ { In }^{ - } \right] }{ \left[ H-In \right] } $$ $$ \left[ { H }_{ 3 }{ O }^{ + } \right] = { K }_{ In }\frac { \left[ H-In \right] }{ \left[ { In }^{ - } \right] } \qquad ...(3) $$ $$ \left[ { H }_{ 3 }{ O }^{ + } \right] = { K }_{ In }\frac { \left[ Unionized \ form \right] }{ \left[ Ionized \ form \right] } $$ This clearly indicates that in acidic solution the colour of indicator is due to Unionized form of Indicator. Similarly in basic solutions colour of indicator is due to Ionizaed form. The above equation can also be represented in terms of pH as follows $$ pH = p{ K }_{ In } + log\frac { \left[ { In }^{ - } \right] }{ \left[ H-In \right] } \qquad ...(4)$$ In general when $$ \frac { \left[ { In }^{ - } \right] }{ \left[ H-In \right] } = 10 $$ equation (3) reduces to $$ pH = p{ K }_{ In } + 1 $$ On the other hand if $$ \frac { \left[ H-In \right] }{ \left[ { In }^{ - } \right] } =10 $$ equation (3) reduces to $$ pH = p{ K }_{ In } - 1$$ Therefore the colour change interval is given by $$ pH = p{ K }_{ In } \pm 1\qquad ...(5) $$ This is the range in which the indicator changes its colour from one form to another.
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