How do we convert ppm to $ mol.{L^{ - 1}} $ ?

Hint: Ppm is known as parts per million and mol/L is the unit for Molarity. Both ppm and molarity are measures of concentrations. Ppm can be used in different ways depending on the context. For dilute solutions, 1 ppm can be estimated as 1mg of the solute dissolved in 1 L of water or $ 1mg/L $

Complete Step By Step Answer:
Molarity is the molar concentration which gives us the no. of moles of solute in 1L of the solution. Many concentration units make use of the no. of moles when we’re dealing with large no. of molecules. There are $ 6.022 \times {10^{23}} $ molecules/atoms in one mole.
Parts per million (ppm) indicated the no. of parts of the solute/substance in a million parts of solution. Parts can have any unit, but generally considered in mass units only. Ppm tells you how many grams / milligrams of solute is available for each million grams of the solvent ( in here water). We can give it as: 1 g solute / 10,00,000 g of solvent.
If we are considering water, it has a density of 1 g/mL. Therefore, we can rewrite it as:
1 g solute/ 10,00,000 mL water.
We will divide it by 1000 to convert mL to L: 1 g solute/ 1000L water.
Dividing numerator and denominator by 1000, the ratio obtained is: 1 mg of solute / 1 L of water
Hence we can say that 1 mg in 1 L water is the same as 1 mg in 10,00,000 mg of water, or 1 ppm.
To convert ppm to mol/L, you’ll need to know one thing that is Molar Mass of the solute. The formula for converting ppm to mol/L can be given as:
 $ ppm = \dfrac{{mol}}{L} \times Molar{\text{ }}Mass \times 1000 $

Note:
If you have the Molarity (mol/L) and want to convert it to ppm, first multiply it with molar mass (g/mol), we’ll get the answer in g/L. multiply it by 1000 to convert it into mg/L (converting grams to mg) which is the ppm ( i.e. mg/L)