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Question: \(K_{a1},K_{a2}\) and \(K_{a3}\) are the respective inisation constants for the following reactions:...

Ka1,Ka2K_{a1},K_{a2} and Ka3K_{a3} are the respective inisation constants for the following reactions:

H2SH_{2}S H++HS−H^{+} + HS^{-}

HS−HS^{-} H++S2−H^{+} + S^{2 -}

H2SH_{2}S 2H++S2−2H^{+} + S^{2 -}

The correct relationship between Ka1,Ka2K_{a1},K_{a2} and Ka3K_{a3}is.

A

Ka3=Ka1×Ka2K_{a3} = K_{a1} \times K_{a2}

B

Ka3=Ka1+Ka2K_{a3} = K_{a1} + K_{a2}

C

Ka3=Ka1−Ka2K_{a3} = K_{a1} - K_{a2}

D

Ka3=Ka1/Ka2K_{a3} = K_{a1}/K_{a2}

Answer

Ka3=Ka1×Ka2K_{a3} = K_{a1} \times K_{a2}

Explanation

Solution

: For the reaction:

H2SH_{2}S H++HS−;Ka1H^{+} + HS^{-};K_{a1}

Ka1=[H+][HS−][H2S]K_{a1} = \frac{\lbrack H^{+}\rbrack\lbrack HS^{-}\rbrack}{\lbrack H_{2}S\rbrack} …. (i)

For the reaction:

HS−HS^{-} H++S2−;Ka2H^{+} + S^{2 -};K_{a2}

Ka2=[H+][S2−][HS−]K_{a2} = \frac{\left\lbrack H^{+} \right\rbrack\left\lbrack S^{2 -} \right\rbrack}{\left\lbrack HS^{-} \right\rbrack} ….(ii)

For the reaction:

H2SH_{2}S 2H++S2−;Ka32H^{+} + S^{2 -};K_{a3}

Ka3=[H+]2[S2−][H2S]K_{a3} = \frac{\left\lbrack H^{+} \right\rbrack^{2}\left\lbrack S^{2 -} \right\rbrack}{\left\lbrack H_{2}S \right\rbrack}

By multiplying eqn. (i) and eqn. (ii), we get …(iii)

Ka1×Ka2=[H+][HS−][H2S]×[H+][S2−][HS−]K_{a1} \times K_{a2} = \frac{\left\lbrack H^{+} \right\rbrack\left\lbrack HS^{-} \right\rbrack}{\left\lbrack H_{2}S \right\rbrack} \times \frac{\left\lbrack H^{+} \right\rbrack\left\lbrack S^{2 -} \right\rbrack}{\left\lbrack HS^{-} \right\rbrack}

=[H+]2[S2−][H2S]=Ka3= \frac{\left\lbrack H^{+} \right\rbrack^{2}\left\lbrack S^{2 -} \right\rbrack}{\left\lbrack H_{2}S \right\rbrack} = K_{a3}