A 200 ppm protein solution is diluted 1:10. What is the concentration of the diluted solution in mg/ml and μg/100 ml?

Answer 1

So unit conversions are easiest when broken down or visualized. 200 ppm means 200 parts per million. We can view this as a percentage to make it more relatable: 200/1000000 = 0.0002 = 0.02% . So, if we have a concentration of 200 ppm, we know that 0.02% of that substance by mass is the protein of interest.

If we dilute the protein solution 1:10, that means we dilute it 10 fold. The concentration will therefore be 1/10 of the original concentration. 200ppm * (1/10) = 20ppm.

Finding the concentration will be easiest if we just assume an arbitrary volume. Lets say 1000 mL of solution (which weighs ~1000g since the density of water is 1 g/mL). To find the amount of mg of protein per ml of solution, we multiply our arbitrary volume by the percentage of protein. 20 ppm = 20/1000000 = 0.00002

1000 g * 0.00002 = 0.02g

So we have 0.02g per 1000mL.

0.02g/1000mL = 20mg/1000mL = 0.02mg/mL

Now we need to convert to ug/100mL. Lets start by making the numerator in units of ug by multiplying by 1000.

0.02mg/mL = 20ug/mL. So we have the concentration in micrograms per 1 mL, now we multiply 100 to get micrograms per 100 mL.

20ug/mL * 100 = 2000 ug/100mL