Phenolphthalein is an indicator and is represented by the formula $$\(\mathrm{HIn}\)$$. Phenolphthalein, HIn, is a weak acid. $$\[ \mathrm{HIn} \rightleftharpoons \mathrm{H}^{+}+\mathrm{In}^{-} \]$$ The $$\(K_{\mathrm{a}}\)$$ value for phenolphthalein is $$\(5.0 \times 10^{-10} \mathrm{~mol} \mathrm{dm}^{-3}\)$$ at $$\(298 \mathrm{~K}\)$$. This indicator changes colour at a $$\(\mathrm{pH}\)$$ of approximately $$\(8.8\)$$. Calculate the ratio $$\(\frac{\left[\mathrm{In}^{-}\right]}{[\mathrm{HIn}]}\)$$ at $$\(\mathrm{pH} 8.8\)$$. $$\[ \text { ratio } \frac{\left[\mathrm{In}^{-}\right]}{[\mathrm{HIn}]}=.................... \]$$

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