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Example 3.22: Calculation of Percent by Mass

A 5.0-g sample of spinal fluid contains 3.75 mg (0.00375 g) of glucose. What is the percent by mass of glucose in spinal fluid?

Solution

\(m_{\mathrm{sample}}\) \(= 5.0\ \mathrm{g}\)


\(m_{\mathrm{glucose}}\) \(= 3.75\ \mathrm{mg}\)


The spinal fluid sample contains roughly 4 mg of glucose in 5000 mg of fluid, so the mass fraction of glucose should be a bit less than one part in 1000, or about 0.1%. Substituting the given masses into the equation defining mass percentage yields:

\(f_{\mathrm{glucose}}\) \(= \dfrac{m_{\mathrm{glucose}}}{m_{\mathrm{sample}}} \cdot 100\ \mathrm{％}\)

\(\ \ \ =\dfrac{3.75\ \mathrm{mg}}{5.0\ \mathrm{g}} \cdot 100\ \mathrm{％}\)

\(\ \ \ =7.50\times 10^{-4} \cdot 100\ \mathrm{％}\)

\(\ \ \ =0.075\ \mathrm{％}\)


The computed mass percentage agrees with our rough estimate (it’s a bit less than 0.1%).
Note that while any mass unit may be used to compute a mass percentage (mg, g, kg, oz, and so on), the same unit must be used for both the solute and the solution before you can cancel the mass units, yielding a dimensionless ratio.