Exercises: Solutions and preparation

In the laboratory, an aqueous solution is to be prepared by dissolving exactly $4.00\,\text{g}$ of pure sodium hydroxide, $\mathrm{NaOH}$, in deionized water to a total volume of $250.0\,\text{mL}$ at $20\,^{\circ}\text{C}$. Atomic mass data: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$.

1. a) Calculate the molar concentration (molarity) of the resulting solution.
2. b) State, with reasoning, which precision volumetric glassware must necessarily be used to set this final volume.

A concentrated solution of hydrochloric acid, $\mathrm{HCl}$, with concentration $2.00\,\text{mol}\times\text{L}^{-1}$, is available in the lab. Exactly $500.0\,\text{mL}$ of a dilute solution of $\mathrm{HCl}$ with concentration $0.050\,\text{mol}\times\text{L}^{-1}$ is required.

1. a) Calculate the volume of concentrated solution that must be measured out to carry out this dilution.
2. b) From the point of view of good lab practice and safety, explain which auxiliary instrument must necessarily be attached to the pipette to take the aliquot and which risky practice is strictly forbidden.

A commercial bottle of concentrated nitric acid, $\mathrm{HNO}_3$, states on its label a purity of $65.0\,\%$ by mass and a density of $1.40\,\text{g}\times\text{cm}^{-3}$ at $20\,^{\circ}\text{C}$. Atomic mass data: $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{N}) = 14.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$.

1. a) Calculate the mass of pure nitric acid present in $1.00\,\text{L}$ of this commercial reagent.
2. b) Determine the molar concentration of this commercial solution.

In the laboratory, a controlled dilution of a stock solution of copper(II) sulfate, $\mathrm{CuSO}_4$, with initial concentration $0.800\,\text{mol}\times\text{L}^{-1}$, is carried out. Using a volumetric pipette, an aliquot of $20.0\,\text{mL}$ is transferred to a volumetric flask of $250.0\,\text{mL}$, which is then made up with deionized water to $20\,^{\circ}\text{C}$. The equipment used and the detail of the final meniscus setting are illustrated below:

1. a) Calculate the final molar concentration of the dilute solution obtained in the volumetric flask.
2. b) A student adds water until the bottom of the meniscus is above the graduation mark when viewed at the level of the mark. Explain whether the real concentration will be higher or lower than the calculated one, and why removing some of that solution down to the mark does not correct its concentration.

Two aqueous solutions of potassium chloride, $\mathrm{KCl}$, are mixed in the lab, with no chemical reaction taking place. Solution A has a volume of $150.0\,\text{mL}$ and a concentration of $0.500\,\text{mol}\times\text{L}^{-1}$. Solution B has a volume of $350.0\,\text{mL}$ and a concentration of $1.200\,\text{mol}\times\text{L}^{-1}$. Assume ideal behavior with strictly additive volumes at $20\,^{\circ}\text{C}$.

1. a) Calculate the final molar concentration of chloride ions, $\mathrm{Cl}^-$, in the resulting mixture.
2. b) Calculate the volume of pure water that would have to be evaporated from the resulting mixture so that the final concentration of $\mathrm{KCl}$ reaches exactly $1.500\,\text{mol}\times\text{L}^{-1}$. In b), compare the volumes at $20\,^{\circ}\text{C}$ and assume that only water is lost, with no precipitation or change in the additivity of volumes.

$500.0\,\text{mL}$ of an aqueous solution of sulfuric acid, $\mathrm{H}_2\mathrm{SO}_4$, $0.250\,\text{mol}\times\text{L}^{-1}$ is to be prepared from a commercial acid of $96.0\,\%$ purity by mass and density $1.84\,\text{g}\times\text{cm}^{-3}$. Atomic masses: $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{S}) = 32.06\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$.

1. a) Calculate the volume of concentrated commercial acid that must be taken.
2. b) Set out the experimental sequence for adding the reagents, justifying in detail the specific safety rule for avoiding serious thermal accidents.

In a quality control laboratory, the preparation of $100.0\,\text{mL}$ of a standard solution of primary anhydrous sodium carbonate, $\mathrm{Na}_2\mathrm{CO}_3$, at a nominal concentration of $0.0500\,\text{mol}\times\text{L}^{-1}$ at $20\,^{\circ}\text{C}$ is standardized. An analytical balance with uncertainty $\pm 0.001\,\text{g}$ and a class A volumetric flask of $100.0\,\text{mL}$ with calibration tolerance $\pm 0.10\,\text{mL}$ are available. Atomic masses: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{C}) = 12.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$.

1. a) Calculate the theoretical mass of solute that must be weighed to obtain exactly the specified concentration.
2. b) Determine the total relative uncertainty in the molarity by propagating the maximum absolute uncertainties of weighing and volume, and express the final result with its uncertainty interval: $M \pm \Delta M$. For this estimate, use the conservative approximation $\Delta M/M=\Delta m/m+\Delta V/V$ and treat the molar mass as exact.

Exactly $1.000\,\text{L}$ of an aqueous solution of sodium chloride, $\mathrm{NaCl}$, with a final concentration of $0.750\,\text{mol}\times\text{L}^{-1}$ at $20\,^{\circ}\text{C}$ must be prepared. Three sources of the reagent are available in the lab: solution 1 ($200.0\,\text{mL}$ of $\mathrm{NaCl}$ $0.400\,\text{mol}\times\text{L}^{-1}$), solution 2 ($300.0\,\text{mL}$ of $\mathrm{NaCl}$ at $4.50\,\%$ by mass with density $1.03\,\text{g}\times\text{cm}^{-3}$) and a jar of $\mathrm{NaCl}$ solid anhydrous of $98.0\,\%$ purity by mass. Atomic masses: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{Cl}) = 35.45\,\text{g}\times\text{mol}^{-1}$.

1. a) Calculate the amount of substance (moles) of $\mathrm{NaCl}$ contributed jointly by solutions 1 and 2.
2. b) Calculate the mass of impure solid reagent that must be weighed to make up the necessary moles, placing it in the $1.000\,\text{L}$ volumetric flask before finally making up to the mark with deionized water.

A technician tries to prepare $500.0\,\text{mL}$ of standard solution of $\mathrm{NaOH}$ $0.1000\,\text{mol}\times\text{L}^{-1}$ by weighing $2.000\,\text{g}$ of commercial pellets and making up to the mark with deionized water in a volumetric flask. When this solution is subsequently titrated against potassium hydrogen phthalate (primary standard), the real molarity obtained is found to be only $0.0885\,\text{mol}\times\text{L}^{-1}$. Atomic masses: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$.

1. a) Assuming that the volume was made up exactly to $500.0\,\text{mL}$, and that the impurities present in this batch are water and substances that do not react in the titration, determine the real percentage purity in $\mathrm{NaOH}$ of the commercial pellets used.
2. b) Explain, with reasoning, two chemical and experimental reasons why solid $\mathrm{NaOH}$ can never be considered a direct primary standard, and justify why it is necessary to carry out a standardization titration.