If we use phenolphthalein as an indicator in a titration of $Na_2CO_3$ with $HCl$,the usual result is:

Indicator for the titration of $HCl$ and $Na_2CO_3$ would be

For an acid indicator with $K_{in} = 1.0 \times 10^{-5}$, the color change occurs when the concentration of the indicator is $1 \times 10^{-3} \ M$. Find the $pH$ at which the color change occurs.

In base $vs.$ acid titration,at the end point,methyl orange is present as:

Phenolphthalein is the most suitable indicator for the titration of:

In an acid-base titration,the rapid change in $pH$ near the equivalence point depends on the indicator used. The $pH$ of the solution is related to the ratio of the concentrations of the conjugate acid $(HIn)$ and base $(In^-)$ forms of the indicator by which equation?