Equilibrium Constant $Ka$​

Huaxue/Xимия.

Basics

\[1M = 1\frac{mol}{L} \]

the unit of \([X]\) is \(M\).

\[pH = -log_{10}[H^+] \]

\(HA \to H^+ + A^-\). A strong acid/base doesn't have a dissociation constant, the \([H^+]\) is just \([HA]\)(concentration), which is trivial.

Dissociation Constant \(Ka\)​

\[K_a = \frac{[H^+][A^-]}{[HA]} \]

\(HA \rightleftharpoons H^+ + A^-\)

Set \(x\) as concentration \([H⁺]\)

\[K_a = \frac{x*x}{C-x} \]

while \(x << C\), \(C\) is \([HA]\)

\[K_a \approx \frac{x*x}{C} \]

\[x \approx \sqrt{C K_a} \]

\(HA + OH^- \rightleftharpoons H_2O + A^-\)

\[K_a = \frac{[H^+][A^-]}{[HA]} \]

\[K_a = \frac{x(C_b+x)}{C_a-x} \]

while \(x << C_a, C_b\)(*),

\[K_a \approx \frac{x*C_b}{C_a} \]

\[x \approx K_a \frac{C_a}{C_b} \]