Question

A solid sample contains about 200ppm (w/w) of Ca. How many mg of sample must be dissolved in 100mL in order to give a solution that is about 1ppm (w/v) of Ca after dilution?

Answer 1

We need to add
`5 * 10^(-4)` mg

Step-by-step explanation:

Remember first:

`ppm(w/w) = (g_(solute))/(g_(solution))* 10^(-6)\\ppm(w/v)= (1 g_(solute))/(1000mL_(solution))\\g_s= grams\ of\ sample\\mL_s= mL\ of\ sample`

To calculate this mass, we need to calculate the concentration as follows:

`(x\ mg_s)/(100mL_s) * (1g_s)/(1000 mg_s) * (200gCa)/(g_s) * 10^6= 2000x (gCa)/(mL_s)`

Here we have the concentration of the sample in terms of x, being x the mg needed to have a solution of 1ppm (w/v). Therefore, we solve the system as follows:

`2000x (gCa)/(mL_s)=(1gCa)/(1000mL_s)\\x= (1mL_s)/(2000* 1000)= 5* 10^(-7) g= 5* 10^(-4) mg`

Finally we need
`5* 10^(-4)` mg of sample to have a Ca concentration of 1ppm (w/v) in the final solution.