Exercises: Mole, composition and measurement

A sample of $44.10\text{ g}$ of propane gas ($\mathrm{C_3H_8}$) is placed in a closed container.

1. a) Calculate the amount of substance of propane contained in the container and determine the total number of propane molecules present.
2. b) Calculate the number of moles of hydrogen atoms and the absolute number of hydrogen atoms present in the sample.

Data: Atomic molar masses: $\mathrm{C} = 12.01\text{ g}\times\text{mol}^{-1}$; $\mathrm{H} = 1,008\text{ g}\times\text{mol}^{-1}$. Avogadro constant: $N_{\mathrm{A}} = 6,022\times 10^{23}\text{ mol}^{-1}$.

Natural gallium consists exclusively of two stable isotopes: $^{69}\mathrm{Ga}$, with isotopic mass $68,926\text{ u}$ and a natural abundance of $60.11\,\%$, and $^{71}\mathrm{Ga}$, with isotopic mass $70,925\text{ u}$ and an abundance of $39.89\,\%$.

1. a) Calculate the weighted mean relative atomic mass of gallium, giving the result to four significant figures.
2. b) Briefly explain why the atomic mass given in the periodic table for chemical elements rarely coincides with an exact integer.

In a laboratory test, an analytical balance with an absolute uncertainty of $\pm 0.0001\text{ g}$ is used. The watch glass is first tared and a portion of sodium chloride ($\mathrm{NaCl}$) is weighed, with a reading of $2.3376\text{ g}$ recorded on the display.

1. a) State the number of significant figures of this mass measurement and express the weighing result together with its associated absolute uncertainty.
2. b) Calculate the amount of substance (in moles) of $\mathrm{NaCl}$ weighed, giving the result to the correct number of significant figures.

Data: Atomic molar masses: $\mathrm{Na} = 22.99\text{ g}\times\text{mol}^{-1}$; $\mathrm{Cl} = 35.45\text{ g}\times\text{mol}^{-1}$.

In the laboratory, a pure anhydrous sample of copper(II) sulfate, $\mathrm{CuSO_4}$, is weighed. To avoid direct contact with the pan of the single-pan digital balance, a clean watch glass is used. First the empty watch glass is read, and then the solid crystalline salt is placed on it, giving the readings shown in the following instrument diagram:

Using the experimental measurements shown:

1. a) Calculate the net mass of $\mathrm{CuSO_4}$ and the amount of substance weighed, rounding to the correct number of significant figures.
2. b) Determine the number of formula units of $\mathrm{CuSO_4}$ weighed and the total number of oxygen atoms present in that portion.

Data: Atomic molar masses: $\mathrm{Cu} = 63.55\text{ g}\times\text{mol}^{-1}$; $\mathrm{S} = 32.06\text{ g}\times\text{mol}^{-1}$; $\mathrm{O} = 16.00\text{ g}\times\text{mol}^{-1}$. Avogadro constant: $N_{\mathrm{A}} = 6,022\times 10^{23}\text{ mol}^{-1}$. Reading of the empty glass: $15,320\text{ g}$; reading with sample: $19,795\text{ g}$.

Quantitative elemental analysis of a pure sample of an open-chain carboxylic acid shows a percentage composition by mass of $40.00\,\%$ carbon, $6.71\,\%$ hydrogen and $53.29\,\%$ oxygen. By a complementary physical method, its molar mass is found to be $90.08\text{ g}\times\text{mol}^{-1}$.

1. a) Determine, with justification, the empirical formula of this organic compound.
2. b) Deduce its molecular formula and propose a compatible semi-structural formula containing one carboxyl group and one hydroxyl group.

Data: Atomic molar masses: $\mathrm{C} = 12.01\text{ g}\times\text{mol}^{-1}$; $\mathrm{H} = 1,008\text{ g}\times\text{mol}^{-1}$; $\mathrm{O} = 16.00\text{ g}\times\text{mol}^{-1}$.

Iron(II) sulfate usually crystallises as the heptahydrate, $\mathrm{FeSO_4\times 7H_2O}$. In a gravimetry practical, the starting point is a pure crystal of this salt with a mass of $6,950\text{ g}$.

1. a) Calculate the mass fraction and the percentage by mass of water of crystallisation present in the compound.
2. b) Determine the total amount of substance of oxygen atoms present in the $6,950\text{ g}$ of salt, specifying how many moles of these atoms come from the water of hydration molecules and how many come from the sulfate anion.

Data: Atomic molar masses: $\mathrm{Fe} = 55.85\text{ g}\times\text{mol}^{-1}$; $\mathrm{S} = 32.06\text{ g}\times\text{mol}^{-1}$; $\mathrm{O} = 16.00\text{ g}\times\text{mol}^{-1}$; $\mathrm{H} = 1,008\text{ g}\times\text{mol}^{-1}$.

A gaseous volatile organic compound consists only of carbon, hydrogen and nitrogen. Complete combustion of a sample of $1,452\text{ g}$ of this substance produces $2,201\text{ g}$ of $\mathrm{CO_2}$ and $1,351\text{ g}$ of $\mathrm{H_2O}$, with all the nitrogen being converted into gaseous diatomic nitrogen ($\mathrm{N_2}$).

Separately, a sample of $0.5900\text{ g}$ of the same compound is placed in a closed flask of $311.0\text{ mL}$ at a constant temperature of $100.0\,^\circ\mathrm{C}$, reaching an equilibrium pressure of $1,000\text{ atm}$. Assuming ideal gas behaviour:

1. a) Determine the mass of each element in the combusted sample and deduce the empirical formula.
2. b) Calculate the experimental molar mass of the gas and determine its definitive molecular formula.

Data: $R = 0.08206\text{ atm}\times\text{L}\times\text{mol}^{-1}\times\text{K}^{-1}$. Atomic molar masses: $\mathrm{C} = 12.01\text{ g}\times\text{mol}^{-1}$; $\mathrm{H} = 1,008\text{ g}\times\text{mol}^{-1}$; $\mathrm{N} = 14.01\text{ g}\times\text{mol}^{-1}$; $\mathrm{O} = 16.00\text{ g}\times\text{mol}^{-1}$.

Natural boron has a mean atomic mass of $10,811\text{ u}$ and is composed only of two stable isotopes: $^{10}\mathrm{B}$, with isotopic mass $10.0129\text{ u}$, and $^{11}\mathrm{B}$, with isotopic mass $11.0093\text{ u}$.

1. a) Set up the corresponding system of equations and determine, to four significant figures, the percentage natural abundance of each of the two isotopes.
2. b) In a piece of pure elemental boron of $2.7028\text{ g}$, calculate the mass due exclusively to the isotope $^{10}\mathrm{B}$ and the total number of neutrons contributed jointly by all the $^{10}\mathrm{B}$ atoms contained in that piece.

Data: Atomic number of boron: $Z = 5$. Avogadro constant: $N_{\mathrm{A}} = 6,022\times 10^{23}\text{ mol}^{-1}$.

A solid sample of $5.0000\text{ g}$ consisting exclusively of a homogeneous mixture of sodium chloride ($\mathrm{NaCl}$) and calcium carbonate ($\mathrm{CaCO_3}$) is subjected to prolonged calcination in an open crucible. At the working temperature, the sodium chloride remains unchanged, whereas the calcium carbonate decomposes completely on heating, releasing carbon dioxide gas according to the reaction: $\mathrm{CaCO_3(s) \rightarrow CaO(s) + CO_2(g)}$.

After cooling the crucible in a desiccator containing silica gel to avoid absorption of atmospheric moisture, the dry solid residue has a final mass of $3.8998\text{ g}$.

1. a) Calculate the mass of $\mathrm{CaCO_3}$ and of $\mathrm{NaCl}$ present in the initial mixture, as well as the percentage by mass of each component.
2. b) Express the composition of the original mixture as mole fractions and explain, with reasoning, the sign of the error that would be made in the percentage of calcium carbonate if the crucible had been left to cool in the open air without a desiccator.

Data: Atomic molar masses: $\mathrm{Ca} = 40.08\text{ g}\times\text{mol}^{-1}$; $\mathrm{C} = 12.01\text{ g}\times\text{mol}^{-1}$; $\mathrm{O} = 16.00\text{ g}\times\text{mol}^{-1}$; $\mathrm{Na} = 22.99\text{ g}\times\text{mol}^{-1}$; $\mathrm{Cl} = 35.45\text{ g}\times\text{mol}^{-1}$.