1 ppm = 1 part per 10^6 part

= 1 mg solute per 10^6 mg solvent

= 1mg solute per 1 kg solvent

= 1mg solute per 1 kg ethanol

= (0.001 g / 1000g) * 100 = 0.0001 %w/w

= 1 mg / 1266 mL = 0.00079 mg/ml or g/L

[ethanol density = 790 g/L --> 790g = 1000 mL]

So, 200 ppm of SA in ethanol

= 0.02 %w/w

= 0.158 mg/ml

= dissolve 1.6 mg in 10ml ethanol.

Hope this clarifies.

Note: 1ppm = 1mg/L --> applicable for solvents with density like that of water.

Part II (conversion of mass solvent to volume solvent to %)

For sake of simplicity we assume that the 10^6 part is the solvent.

Divide 1 kg of solvent by density of solvent at temperature that you prepare and use your solution.

In order to convert mg/L to % (w/v) (more practical if state of solute is solid) we need to divide mg by 10^6 mg/kg and multiply with 100%.

Example (stearic acid in ethanol):

200 ppm = 200 mg / 10^6 mg = 200 mg / kg

(200 mg / kg) / (0.789 g / mL) = 253 mg / L

(253 mg / L) / (10^6 mg / kg) x 100 % = 0.0253 % (w/v)

parts per million (ppm) is 1 part solute ( in ur case stearic acid) in 10^6 parts of solvent (in u want to dissolve stearic acid).

% wt is 1 part ( in wt terms) in 100 parts and % vol is 1 part ( in vol terms) in 100 parts of solvent.