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Two weak monobasic organic acids HA and ...

Two weak monobasic organic acids `HA` and `HB` have dissociation constans as `3.0 xx 10^(-5)` and `1.5 xx 10^(-5)`, respectively, at `25^(@)C`. If `500mL` of `1M` solutions of each of these two acids are mixed top product `1L` of mixed acid solution, what iws the `pH` of the resulting solutions?

Text Solution

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Note that `K_(a)` of two acids is nearly same . In such cases , we have to consider `H^(+)` from both HA and HB simultaneously . The concentration of HA and HB in the mixture = `0.5` M [ equal volumes are mixed ] = say c.
` HA to H^(+) +A^(-)`
`HB to H^(+) +B^(-)`
Let x = `[H^(+)] ` from HA and Y = `[H^(+)] ` from HB
`rArr [ H^(+)] _("final") = x+y`
`K_(HA) = ((x+y)x)/c and K_(HB) = ((x+y)y)/c`
` 15/18 = x/y rArr 6x = 5y `
Substitute for ` y = 6/5 x " in " K_(HA) = (x^(2)+xy)/c `
` rArr 1.5 xx10^(-5) = (5x^(2)+6x^(2))/(2.5)`
` x = 1.84 xx10^(-3), y = 2.21 xx10^(-3)`
`[H^(+)] = x+ y = 4.055 xx10^(-3)`
`pH = - log_(10) ( 4.055 xx10^(-3))`
`rArr pH = 2.392 `
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