Question

How many mL of a solution of concentration 100 mg $C{o}^{2+}$ per mL is needed to prepare 10 mL of a solution of concentration 20 mg $C{o}^{2+}$ per mL ?

Answer 1

Atomic weight of $Co=58.93g$.
Number of moles of $C{o}^{2+}$ in 100 mg sample $=\frac{100mg}{58.93g/mol}=\frac{100}{58.93}millimoles$
The concentration of solution will be $C_1=\frac{\frac{100}{58.93}millimoles}{1ml}=\frac{100}{58.93}M$.
Number of moles of $C{o}^{2+}$ in 20 mg sample $=\frac{20mg}{58.93g/mol}=\frac{20}{58.93}millimoles$
The concentration of solution will be $C_1=\frac{\frac{20}{58.93}millimoles}{1ml}=\frac{20}{58.93}M$.
The relationship between the concentration and the volume of the solution is $C_1{V}_1=C_2{V}_2$
$\frac{100}{58.93}M\times V_1=\frac{20}{58.93}M\times 10mL$
$V_2=\frac{20\times 10}{100}=2mL$.
Hence, 20 mL of a solution of concentration 100 mg $C{o}^{2+}$ per mL is needed to prepare 10 mL of a solution of concentration 20 mg $C{o}^{2+}$ per mL.