a Brønsted Lowry acid is a proton donor and an Brønsted Lowry base is a proton acceptor. reactions between these 2 types of molecules involve a transfer of a proton between the 2 species. an example of this is the solvation of hydrogen chloride in water to make hydrochloric acid
$$ \ce{HCL + H2O->Cl- + H3O+} $$
the interaction of a solute with the solvent is called solvation. the solvent will form a solvation shell around the solute molecules via non-covalent interactions
the higher the charge density on the solute the larger the solvation shell as it will interact with more of the solvent. these solvation shells can be made up of multiple layers depending on the charge density and are always in motion, with the solvent molecules being constantly replaced
protic solvents
protic solvents like MeOH, EtOH and water contain OH group that can act as a source of protons in reactions and form hydrogen bond
aprotic solvents
aprotic solvents do not contain any protons that can be donated. examples include propanone, ethanenitrile
although mst acid base reaction occur in the aquesous state, gasseous reactions can also occur such as that between $\ce{NH3}$ and $\ce{HCl}$ gasses-
$$ \ce{HCl_{(g)} + NH3_{(g)} -> NH4+Cl-_{(s)}} $$
weak acids and bases dissolve in water in an equilibrium between their undissociated forms and their conjugate forms.
$$ \ce{\underbrace{CH3COOH}{\text{acid}}+ \underbrace{H2O}{\text{base}} <=> \underbrace{CH3COO-}{\text{conjugate base}} + \underbrace{H3O+}{\text{conjugate acid}}} $$
$\ce{H3O}$ can be seen as a conjugate base as it donates to proton to $\ce{CH3COO-}$ to form its base form of $\ce{H2O}$ and the undissociated acid $\ce{CH3COOH}$
the same happens with weak bases like $\ce{ NH3}$. the water acts as a base and donates a proton to ammonia to form the ammonium ion and a hydroxide ion
$$ \ce{\underbrace{NH3}{base}+\underbrace{H2O}{acid}<=>\underbrace{OH-}{conjugate base}+\underbrace{NH4+}{conjugate acid}} $$
we know that strong acids fully dissociate in water whereas weak acids only partially dissociate and that the measure of an acids strength is its $K_a$ value.
$$ \ce{\frac{[H3O][A-]}{[HA]}=K_a} $$
because this number can be both very large and very small depending on the acid, we use a logarithmic scale to understand and compare them more easily
a high $K_a$ value indicates a very strong acid
a high $pK_a$ value indicates a very weak acid
$$ \ce{pK_a=-log(K_a) } $$
$$ K_a= 10^{-pK_a} $$
now we are in university we have to do more maths and so lets take a look into that $pK_a$ equation. its not quite right because we cant take the logarithm of a value with units. therefore we use the thermodynamic equilibrium constant, $\bold{K}$.
apprently we need to use thsi equation instead, where $a_A$ is the activity of A and $[A]^{\minuso}$ has no units
$$ a_A=\frac{[A]}{[A]^{\minuso}} $$