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Convert Parts per Million to Moles

How do I convert a parts per million measurement of Hydrogen Sulfide content in Sulfur into moles?

Answer: You need some additional information about the substances you are trying to convert. In the future, we hope to provide a calculator for this that will make the calculation easy!

Explanation: You need to know the molar mass of Hydrogen Sulfide and the molar mass of Sulfur, and the mass of the sample you are trying to convert (or their molar volume and the volume of the solution instead of their molar mass and mass of the solution). Let's say that you have 100 parts of Hydrogen Sulfide per million parts of solution, and assuming that the molar mass of Hydrogen Sulfide is 3 kilograms per mole and the molar mass of Sulfur is 4 kilograms per mole (these are **not** the actual values), and assume that you have 5 kilograms of the mixed substance. You need to solve

3 X + 4 Y = 5

and

100 / X = (1,000,000 - 100) / Y

for X and Y. X is the number of moles of Hydrogen Sulfide and Y is the number of moles of Sulfur. Multiply both sides by Y:

100 Y / X = (1,000,000 - 100)

simplify 1,000,000 - 100:

100 Y / X = 999,900

divide both sides by 100:

Y / X = 999,900 / 100

simplify 999,900 / 100:

Y / X = 9,999

multiply both sides by X:

Y = 9,999 X

substitute the results of the first equation into the second equation:

3 X + 4 (9,999 X) = 5

simplify 4 * 9,999:

3 X + 39,996 X = 5

factor X out of 3 X + 39,996 X:

(3 + 39,996) X = 5

simplify 3 + 39,996:

39,999 X = 5

divide both sides by 39,999:

X = 5 / 39,999

and simplify 5 / 39,999:

X = 1.25003125078126953173829345733643e-4

and substitute the value for X into Y = 9,999 X and simplify:

Y = 1.2499062476561914047851196279907

This means that you have .00012500312... moles of Hydrogen Sulfide and 1.24990624... moles of Sulfur in that 5 kilogram sample.

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