Question 10.13: The concentration of Mg^2+ ion present in a blood sample is ......
The concentration of Mg^{2+} ion present in a blood sample is 4.2 mEq/L. How many milligrams of Mg^{2+} ion are present in 250.0 mL of the blood?
Step 1: The given quantity is 250.0 mL of solution and the desired quantity is milligrams of Mg^{2+} ion.
250.0 mL blood = ? mg Mg^{2+} ion
Step 2: The pathway for solving the problem is
\boxed{mL \ blood }\longrightarrow\boxed{ L \ blood}\longrightarrow\boxed{ mEq \ Mg^{2+} }\longrightarrow\boxed{ Eq \ Mg^{2+}}\longrightarrow\boxed{moles \ Mg^{2+}}\longrightarrow\boxed{g \ Mg^{2+}}\longrightarrow\boxed{ mg \ Mg^{2+}}The mathematical setup, in terms of conversion factors, is
250.0 \ \cancel{mL \ blood}\times \frac{10^{3-} \ \cancel{L \ blood}}{1 \ \cancel{mL \ blood}}\times \frac{4.2 \ \cancel{mEq \ Mg^{2+}}}{1 \ \cancel{L \ blood}}\times \frac{10^{-3} \ \cancel{Eq \ Mg^{2+}}}{1 \ \cancel{mEq \ Mg^{2+}}}\times \frac{1 \ \cancel{mole \ Mg^{2+}}}{2 \ \cancel{Eq \ Mg^{2+}}}\times \frac{24.31 \ \cancel{g \ Mg^{2+}}}{1 \ \cancel{mole \ Mg^{2+}}}\times \frac{1 \ mg \ Mg^{2+}}{10^{-3} \ \cancel{g \ Mg^{2+}}}= 13 mg Mg^{2+}ion
Note the value 2 in the fourth conversion factor. The 2 is needed because of the +2 charge on the Mg^{2+} ion; there are 2 equivalents per mole. The next-to-last conversion factor, relating grams and moles, is based on the atomic mass of magnesium. One mole of magnesium has a mass of 24.31 grams (Section 6.3). [Note that the mass of a Mg^{2+} ion and that of a Mg atom are considered to be the same; their difference in mass is that of 2 electrons and that mass difference is negligible in terms of significant figures (Section 2.5).]