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DavePhD
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If $pK_a = 4.76$, then $K_a = 1.74 \times 10^{-5}$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 1.74 \times 10^{-5}M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$1.74 \times 10^{-5}M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$1.74 \times 10^{-5}M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $

So, for example if pH is 3, $10^{-3}$ is 0.001, so

$1.74 \times 10^{-5} = \frac{10^{-6}M}{c-(10^{-3}M)}$

$1.74 \times 10^{-5}c -1.74 \times 10^{-8}M = 10^{-6}M$

$1.74 \times 10^{-5}c = 1.02 \times 10^{-6}M$

$c = 0.059M$

If $pK_a = 4.76$, then $K_a = 1.74 \times 10^{-5}$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 1.74 \times 10^{-5}M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$1.74 \times 10^{-5}M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$1.74 \times 10^{-5}M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $

If $pK_a = 4.76$, then $K_a = 1.74 \times 10^{-5}$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 1.74 \times 10^{-5}M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$1.74 \times 10^{-5}M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$1.74 \times 10^{-5}M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $

So, for example if pH is 3, $10^{-3}$ is 0.001, so

$1.74 \times 10^{-5} = \frac{10^{-6}M}{c-(10^{-3}M)}$

$1.74 \times 10^{-5}c -1.74 \times 10^{-8}M = 10^{-6}M$

$1.74 \times 10^{-5}c = 1.02 \times 10^{-6}M$

$c = 0.059M$

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DavePhD
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If $pK_a = 4.76$, then $K_a = 57543$$K_a = 1.74 \times 10^{-5}$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 57543M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $$K_a = 1.74 \times 10^{-5}M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$57543M = \frac{[H+]^2}{c-[H+]} $$1.74 \times 10^{-5}M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$57543M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $$1.74 \times 10^{-5}M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $

If $pK_a = 4.76$, then $K_a = 57543$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 57543M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$57543M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$57543M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $

If $pK_a = 4.76$, then $K_a = 1.74 \times 10^{-5}$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 1.74 \times 10^{-5}M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$1.74 \times 10^{-5}M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$1.74 \times 10^{-5}M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $

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DavePhD
  • 41k
  • 2
  • 91
  • 189

If $pK_a = 4.76$, then $K_a = 57543$

Then approximating that $K_a$ can be written in terms of concentration rather than the true definition which is in terms of activities:

$K_a = 57543M = \frac{[A-][H+]}{[HA]} = \frac{[H+]^2}{c-[H+]} $

$57543M = \frac{[H+]^2}{c-[H+]} $

where $c$ is the molar concentration of the vinegar

If you want pH explicitly in the equation, then approximating pH = -log[H+], then:

$57543M = \frac{(10^{-pH}M)^2}{c-(10^{-pH}M)} $