Question

Describe a volumetric dilution procedure that would be more precise than using a$\mathbf{1000}\mathbf{-}\mathbf{\mu L}$micropipette and a$\mathbf{10}\mathbf{-}\mathbf{mL}$volumetric flask. What would be the relative uncertainty in the dilution?

Short answer

A volumetric dilution procedure that would be more precise than using a $1000\mathrm{\mu L}$ micropipette and a $10\mathrm{mL}$volumetric flask are:

• Using a 10mL micropipette and a 100mL volumetric flask: The relative uncertainty in the concentration after dilution using a 10mL micropipette and a 100mL volumetric flask is $0.004680\mathrm{M}\pm 0.2\%$

• Using a 100mL micropipette and a 1L volumetric flask: The relative uncertainty in the concentration after dilution using a 1L micropipette and a 100mL volumetric flask is $0.004680\mathrm{M}\pm 0.09\%$.

Step-by-step solution

About Uncertainty

Uncertainty refers to the inability to forecast a value. The last digit in a measured value will have a related uncertainty. Absolute and relative uncertainties are two types of uncertainties.

Absolute uncertainty:

The marginal value of a measurement was expressed in this way.

Uncertainty in a relative sense compares the extent of absolute uncertainty to the size of the measurement it is connected with.

$\mathrm{Relative}\mathrm{uncertainty}=\frac{\mathrm{absolute}\mathrm{uncertainty}}{\mathrm{magnitude}\mathrm{of}\mathrm{measurement}}$

For a set of measurements having uncertainty values as $e_1,e_2$and $e_3$ the uncertainty $\left(e_4\right)$in addition and subtraction can be calculated as follows:

$e_4=\sqrt{e_1^2+e_2^2+e_3^2}$

Given data

The concentration of the reagent is$0.4680\mathrm{M}$

The relative uncertainty in the dilution of $1000\mathrm{\mu L}\left(1.000\mathrm{mL}\right)$into 10mL is $0.004680\mathrm{M}\pm 0.3\%$.

Find the more precise volumetric dilution

Using a 10mL micropipette and a 100 mL volumetric flask:

Consider the dilution offrom a micropipette into a 100 mL volumetric flask.

Use the tolerance for the volumetric flask from table$2-3\left(100\mathrm{mL}\pm 0.08\right)$

Use the tolerance for the micropipette from table$2-5\left(10\mathrm{mL}\pm 0.2\%\right)$

The dilution factor is:

$\mathrm{Dilution}\mathrm{factor}=\frac{{\mathrm{v}}_{\mathrm{fral}}}{{\mathrm{v}}_{\mathrm{initial}}}$

localid="1663568227874" $$\begin{gathered} =\frac{100\mathrm{mL}\pm 0.08}{10\mathrm{mL}\pm 0.2\%} \\ =\frac{100\mathrm{mL}\pm 0.08}{10\mathrm{mL}\pm 0.2\%}\left(\mathrm{Since}[\left(0.08/100\right)\times 100]=0.08\%\right) \\ =10\pm 0.215\%\left(\mathrm{Since}\sqrt{0.{08}^2+0.2^2}=0.215\%\right) \\ =10\pm 0.2\% \end{gathered}$$

The concentration of the dilute solution is:

Concentration of dilute solution$=\frac{0.04680\mathrm{M}}{10\pm 0.2\%}$

$=0.004680\mathrm{M}\pm 0.2\%$

The relative uncertainty concentration is $0.004680\mathrm{M}\pm 0.2\%$

Using a 100mL micropipette and a 1L volumetric flask:

Consider the dilution of 100mL from a micropipette into a 1L volumetric flask.

Use the tolerance for the volumetric flask from table$2-3\left(1000\mathrm{mL}\pm 0.30\right)$

Use the tolerance for the micropipette from table$2-4\left(100\mathrm{mL}\pm 0.08\right)$

The dilution factor is:

role="math" localid="1663568448270" $$\begin{gathered} \mathrm{Dilution}\mathrm{factor}=\frac{{\mathrm{V}}_{\mathrm{fral}}}{{\mathrm{V}}_{\mathrm{initial}}} \\ =\frac{1000\mathrm{mL}\pm 0.30}{100\mathrm{mL}\pm 0.08} \\ =\frac{1000\mathrm{mL}\pm 0.03\%}{\left(100\mathrm{mL}\pm 0.08\%\right)}\left(\mathrm{Since}[\left(0.30/1000\right)\times 100]=0.03\%\right) \\ =10\pm 0.0854\%\left(\mathrm{Since}\sqrt{0.{08}^2+0.{03}^2}=0.854\%\right) \\ =10\pm 0.09\% \end{gathered}$$

The concentration of the dilute solution is:

$$\begin{gathered} \mathrm{concentration}\mathrm{of}\mathrm{dilute}\mathrm{solution}=\frac{0.04680\mathrm{M}}{10\pm 0.09\%} \\ =0.004680\mathrm{M}\pm 0.09\% \end{gathered}$$

The relative uncertainty concentration is $0.004680\mathrm{M}\pm 0.09\%$

Thus, a volumetric dilution procedure that would be more precise than using a $1000\mathrm{\mu L}$ micropipette and a $10\mathrm{mL}$ volumetric flask are:

• Using a 10mL micropipette and a 100mL volumetric flask: The relative uncertainty in the concentration after dilution using a 10mL micropipette and a 100mL volumetric flask is$0.004680\mathrm{M}\pm 0.2\%$

• Using a 100mL micropipette and a 1L volumetric flask: The relative uncertainty in the concentration after dilution using a 100mL micropipette and a 1L volumetric flask is $0.004680\pm 0.09\%$.