Dear Saiful: formally ppm is defined as: mg/L, because for dilute solutions density of solution is equal to unity, the same of the water, then mg/kg(dilute solution) = mg/L. D(water) = 1 Kg/L. Mr. Benson say the true.
mg/Kg is equal to ppm, meaning parts per million. However, mg/L is a density unit. You should not consider 'mg/kg' and 'mg/L' as the same. 4.09 wt% is equal to 40, 900 ppm. There is 13% difference between 40,900 ppm and 47,200 ppm. If so, you need to search more reference to get a confirmed average value.
You have written: 'mg/kg' and 'mg/L' as the same. I have written : for dilute solutions density of solution is equal to unity, "the same of the water", if density "D" is the same of the water, then mg/kg(dilute solution) = mg/L, because 1 L of dlilute solution weighs 1 Kg. You can read over and over and you will never find that afirmation.
But, if you have some doubt, we have treated this topic in Research Gate in the past, but too you can review the bibliography about this issue in books of Básic Chemistry. However, is not the same density(g/ml or Kg/L) to ppm(mg/L), as you would seem to have.
Just explain 'ppm' based on what I understand one more time. At first, Nsikak has provided a perfect answer for Saiful's question. Both of us agree with that. ppm is unitless or its unit is 1, which means 0.0001% (with unit 1). 'ppm' can be used for solid, aqueous solution with density (>,=,
@Manousos-Ioannis Manousakas Is this the shale value or otherwise for Fe? What is the reference? I do not think the value is correct as quoted by Saiful in his question. It is appropriate to understand the matrix (sandstone,shale, carboneous, igneous rock, or deep-sea sediments) to know the specific value to use for his calculation. The comprehensive table for all elements has been attached in my first response. All the same, your explanation is correct but I am not certain of the 40900 mg/kg value.
In dilute solutions, the unit mg/L can be matched to "ppm" as stated by La Rosa. In the case of solids the correct unit is mg/kg. Because the parallel with liquid samples, people use "ppm" as an equivalent unit but this is totally wrong.
On the Fe value you asked, Bowen (1979) gives the value of 4,1% for mean crust. Iron content increases for clay and sediments (Turekian and Whedepol, 1961) and is lower in sandstone and limestone (Bowen, 1979).
@Nsikak Benson I just used the information Saiful provided to help him with the conversion. I am not suggesting that the value quoted is the most appropriate to be used. Just indicating how the conversion is made.
To convert to ppm, it depends on whether the value is given as "Fe" or "FeO". If the former, ppm is simply 5% of a million or 50,000 ppm. If the latter, you must convert FeO to Fe. To do this simply divide the atomic weight of Fe (55.85) by the atomic weight of FeO (71.85) and mutliply your FeO value by the result. For 5% FeO you now have 3.88% Fe or 38,800 ppm. You can do this for any element given (as is typical in geological analysis) as wt.% oxide.
Dear James: A little correction, I quote....To do this simply divide the atomic weight of Fe (55.85) by the "atomic weight" of FeO ....wanted to say " molecular weight or formula weight" FeO.