Unusual Dilution Problem

Question

I have a concentrate of goat mineral mix that is to be added to a 55lb bag of 100% salt. I need to find what the ppm (parts per million) of copper in the final mixture is . The concentrate is 5 lbs. which contains 55,000 ppm of copper. What is the ppm of copper after mixing the concentrate with 50 lbs. of salt? Please show how your answer was found so it can be used to find the other concentrations in the final mixture.

Answer 1

Since we know there are 55,000 lbs of copper for every 1 million lbs of mix, we can say that we have a ratio of:

55,000 lbs of copper/ 1,000,000 lbs of concentrate = 0.055 or 5.5% copper in our goat mineral mix.

I know the concentrate is 5 lbs so the total amount of copper we have in the mix is:

Copper = (% of copper in concentrate)(total mass of concentrate) = 0.055(5lbs) = 0.275 lbs of copper

If we add the 50lbs salt mix, we get a total mixture weight of 50 lbs + 5lbs = 55 lbs.

Then we can divide the actual amount of copper by the total mixture mass to find the percent of copper in the final mix with salt.

% copper in entire mix = (0.275 lbs copper) / (55 lbs of entire mix) = 0.005 which is 0.5%.

Lastly, we convert the percentage to ppm by multiplying by 10^6 as we are finding how much copper there is for every 1 million lbs.

0.005 x 10^6 = 5000 ppm of copper