Therefore, for the dissociation equilibrium of any acid
the acid dissociation constant, Ka, is defined as
Two assumptions are required:
1 The concentrations of H+(aq) and A−(aq) are equal, or in symbols:
The reason this is an approximation is that a very slightly higher concentration of H+(aq) exists in reality, due to the autodissociation of water, H2O(l) ⇌ H+(aq) + A−(aq). We neglect this effect since water produces a far lower concentration of H+(aq) than most weak acids. If you were studying an exceptionally weak acid (you won't at A-level), this assumption might begin to cause big problems.
2 The amount of HA at equilibrium is the same as the amount originally added to the solution.
This cannot be quite true, otherwise HA wouldn't be an acid. It is, however, a close numerical approximation to experimental observations of the concentration of HA in most cases.
![{\displaystyle {\mbox{pH}}=-\log _{10}{\left({\sqrt {K_{a}\left[{\mbox{acid}}\right]}}\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60080f496f7742c4d218dcf684a087c9a01d8120)
![{\displaystyle K={\frac {[{\mbox{C}}]^{c}[{\mbox{D}}]^{d}}{[{\mbox{A}}]^{a}[{\mbox{B}}]^{b}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4b495992a71b709753fac6ae1a81256d2d75890e)
![{\displaystyle K_{a}={\frac {[{\mbox{H}}^{+}{\mbox{(aq)}}][{\mbox{A}}^{-}{\mbox{(aq)}}]}{[{\mbox{HA}}{\mbox{(aq)}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f3683dd50c0cfa026599d8cc321f852060f6fd5)
![{\displaystyle \left[{\mbox{H}}^{+}{\mbox{(aq)}}\right]=\left[{\mbox{A}}^{-}{\mbox{(aq)}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/738f5f79e3f15c210185cb11004666fbb4a540df)
![{\displaystyle \left[{\mbox{HA}}{\mbox{(aq)}}\right]=\left[{\mbox{acid}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea0f0573d12144b71ef41b66ff7d29113d02e091)
![{\displaystyle K_{a}={\frac {[{\mbox{H}}^{+}{\mbox{(aq)}}]^{2}}{[{\mbox{HA}}{\mbox{(aq)}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78858d0f412b1a27fd4afc281f6c6f92d151394f)
![{\displaystyle K_{a}={\frac {[{\mbox{H}}^{+}{\mbox{(aq)}}]^{2}}{[{\mbox{acid}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59c6aa5aaf34d35777a70435e5ecd5817e7f1d13)
![{\displaystyle [{\mbox{H}}^{+}{\mbox{(aq)}}]^{2}=K_{a}\left[{\mbox{acid}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5313fb96712d194ce14537adbf0be82c5751dd10)
![{\displaystyle [{\mbox{H}}^{+}{\mbox{(aq)}}]={\sqrt {K_{a}\left[{\mbox{acid}}\right]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/074fd212a4aa5233c2ddd3449d72247e8f745e14)
![{\displaystyle {\mbox{pH}}=-\log _{10}{\left(\left[{\mbox{H}}^{+}{\mbox{(aq)}}\right]\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f380a2b0ac542c30cd9747420c0ccac2c572b97)