To prepare a very dilute solution, it is advisable to perform successive
dilutions of a single prepared reagent solution, rather than to wcigh a very
small mass or to measure a very small volume of stock chemical. A solution was
prepared by transferring \(0.661 \mathrm{~g}\) of \(\mathrm{K}_{2}
\mathrm{Cr}_{2} \mathrm{O}_{7}\) to a \(250.0\)-mL volumetric flask and adding
water to the mark. A \(1.000-\mathrm{mL}\). sample of this solution. was
transferred to a 500 -mL. volumetric flask and diluted to the mark with water.
Then \(10.0 \mathrm{~mL}\) of the diluted solution was transferred to a 250 -mL.
flask and diluted to the mark with water. (a) What is the final concentration
of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{\text {, in solution? (b) What
}}\) mass of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) is in this final
solution? (The answer to the last question gives the amount that would have
had to have been weighed out if the solution had been prepared directly.)