Question

(a) Uncertainty in formula mass. In an extremely-high precision gravimetric titration, the uncertainty in the formula mass of the primary standard could contribute to the uncertainty of the result. Read about uncertainty in molecular mass in Appendix B. Express the formula mass of potassium hydrogen phthalate, ${\mathrm{C}}_8{\mathrm{H}}_5{\mathrm{O}}_4\mathrm{K}$with its 95% confidence interval based on a rectangular distribution of uncertainty of atomic mass with a coverage factor of k 5 2.

(b) Systematic uncertainty in reagent purity. The manufacturer of potassium hydrogen phthalate states that the purity is 1.000 00 60.000 05. In the absence of further information, we assume that the distribution of uncertainty is rectangular. What standard uncertainty would you use for the purity of this reagent

Short answer

a) Uncertainty in formula mass of potassium hydrogen phthalate is$204.221\pm 0.004\mathrm{g}/\mathrm{mol}$

b) Standard uncertainty for purity is calculated by$=1.00000\pm 0.00003$

Step-by-step solution

Define uncertainty

Uncertainty in formula mass refers to uncertainty that occurs in measuring the atomic mass for chemical calculations. In this theory, it is supposed that the distribution of atomic mass follows a rectangular distribution so that atomic mass tends to lie equally anywhere between the interval from $\overline{\mathrm{x}}-\mathrm{a}$to $\overline{\mathrm{x}}+\mathrm{a}$where ' $\mathrm{a}$' corresponds to uncertainty in the periodic table. Rectangular distribution has standard uncertainty of$\mathrm{a}/\sqrt{3}.$

 Step 2: a) Determine the uncertainty of atomic mass

The molecular formula of potassium hydrogen phthalate is${\mathrm{C}}_8{\mathrm{H}}_5{\mathrm{O}}_4\mathrm{K}$. Write down the atomic mass of C , H, O and and divide it by$\sqrt{3}$as rectangular distribution has standard uncertainty of$\frac{a}{\sqrt{3}}$.

localid="1654843391350" $$\begin{gathered} \mathrm{H}:\frac{1.00794\pm 0.00007}{\sqrt{3}}=1.00794\pm 0.000040 \\ \mathrm{O};\frac{15.9994\pm 0.0003}{\sqrt{3}}=15.994\pm 0.00017 \\ \mathrm{K};\frac{39.0983\pm 0.0001}{\sqrt{3}}=39.0983\pm 0.000058 \\ 8\mathrm{C};8(12.0107\pm 0.00046) \\ =96.0856\pm 0.0037 \\ 5\mathrm{H};5(1.00794\pm 0.000040) \\ =5.0397\pm 0.00020 \\ 4\mathrm{O};4(15.994\pm 0.00017) \\ =63.9976\pm 0.00069 \\ 1\mathrm{K};1(39.0983\pm 0.000058) \\ =39.0983\pm 0.000058 \\ {\mathrm{C}}_8{\mathrm{H}}_5{\mathrm{O}}_4\mathrm{K} \\ \mathrm{x}=\mathrm{uncertainty} \\ =\sqrt{0.{0037}^2+0.{00020}^2+0.{00069}^2+0.{000058}^2} \\ =0.0038 \\ =0.004 \end{gathered}$$

Therefore uncertainty in formula mass of potassium hydrogen phthalate is

$204.221\pm 0.004\mathrm{g}/\mathrm{mol}.$

Step 2: b) Compute the uncertainty of the purity of this reagent.

For obtaining uncertainty using rectangular distribution, divide the given uncertainty by $\sqrt{3}$to determine the standard uncertainty. The formula to verify purity is,

$$\begin{gathered} \mathrm{purity}=\frac{1.00000\pm 0.00005}{\sqrt{3}} \\ =1.00000\pm 0.00003 \end{gathered}$$