The correct statement is: the elementary charge (the magnitude of charge of one electron or proton) is $e = 1.602176634\times10^{-19}\text{ C}$. So 1 coulomb is the charge of about $6.241509074\times10^{18}$ electrons.
Explanation
- First, a clarification: 1 coulomb is not equal to $1.6\times10^{-19}$. Rather, one elementary charge (the charge on a single electron) equals about $1.6\times10^{-19}\text{ C}$. A coulomb is a much larger unit of charge.
- The numerical value of $e$ was determined experimentally (famous early work: the Millikan oil‑drop experiment measured the electron charge). Later, more precise methods (Faraday constant divided by Avogadro’s number, measurements using the quantum Hall effect, shot noise, etc.) refined the value.
- You can see the relation using the Faraday constant $F$ (charge per mole of electrons) and Avogadro’s number $N_A$ (number of particles per mole):
$$e=\frac{F}{N_A}$$
Using $F\approx96485\text{ C/mol}$ and $N_A\approx6.02214076\times10^{23}\text{ mol}^{-1}$ gives $e\approx1.602\times10^{-19}\text{ C}$.
- Since the 2019 SI redefinition, the elementary charge was fixed exactly by definition to
$$e=1.602176634\times10^{-19}\text{ C}$$
so that value is now exact in the SI system.
Example calculation: how many electrons make 1 coulomb?
$$\frac{1\text{ C}}{e}\approx\frac{1}{1.602176634\times10^{-19}}\approx6.241509074\times10^{18}\text{ electrons.}$$
Bottom line: the value $1.602\times10^{-19}\text{ C}$ is the (measured and now defined) amount of electric charge carried by a single elementary charge; 1 coulomb contains roughly $6.24\times10^{18}$ such charges.