Weight percent concentration calculation with partition coefficients

[subopolois]

Homework Statement

what is the weight percent concentration of SO2 in the exsolved aqueous fluid phase that existed with solution if sulphur has ppm by weight of 90. partition coefficient= 47

Homework Equations

partition coefficient- 47= concentration of aqueous fluid/ concentration of solution

The Attempt at a Solution

weight % of sulphur= 32/32+2(16)= 0.5
weight % of oxygen= 0.5
90 ppmw sulphur, since there is 1 mole of sulphur and 2 of oxygen there is 180 ppmw oxygen. for a total of 270 ppmw SO2.
47= 270ppmw/x
x= 270/47
x= 5.74

im not really sure if this is correct, if it isn't could someone point me in the right direction?

 

[nate808]

To calculate the weight percent concentration of SO2 in the exsolved aqueous fluid phase, we can use the following formula:

Weight percent concentration = (mass of SO2 / total mass of solution) x 100%

First, we need to calculate the mass of SO2 in the solution. We know that the weight percent of sulphur in SO2 is 50%, so the mass of sulphur would be 0.5 g per 1 g of SO2. Therefore, in 90 ppmw of SO2, the mass of sulphur would be:

90 ppmw SO2 x (0.5 g S / 1 g SO2) = 45 ppmw S

Next, we need to calculate the total mass of the solution. The partition coefficient, K, is defined as the ratio of the concentration of the aqueous fluid phase to the concentration of the solution. In this case, K = 47, so we can set up the following equation:

47 = concentration of aqueous fluid / concentration of solution

We know that the concentration of the solution would be the sum of the concentrations of sulphur and oxygen, which we can calculate using the weight percent concentrations we already know:

Concentration of solution = (45 ppmw S x (1 g SO2 / 0.5 g S)) + (180 ppmw O x (1 g SO2 / 2 g O)) = 360 ppmw SO2

Now, we can plug in the values for K and the concentration of the solution into the equation above to solve for the concentration of the aqueous fluid:

47 = concentration of aqueous fluid / 360 ppmw SO2

Concentration of aqueous fluid = (47 x 360 ppmw SO2) = 16,920 ppmw SO2

Finally, we can plug this value into the original formula to calculate the weight percent concentration of SO2 in the exsolved aqueous fluid phase:

Weight percent concentration = (16,920 ppmw SO2 / 360 ppmw SO2) x 100% = 4.7%

Therefore, the weight percent concentration of SO2 in the exsolved aqueous fluid phase is approximately 4.7%. I hope this helps clarify the solution for you.