Counting particles by mass: the mole: notes and practice questions

A student investigates the reactions of dilute hydrochloric acid with four different substances: solid sodium carbonate ($Na_2CO_3$), solid copper(II) oxide ($CuO$), magnesium ribbon ($Mg$), and aqueous potassium hydroxide ($KOH$).

(a) Write a balanced chemical equation, including state symbols, for the reaction of hydrochloric acid with solid sodium carbonate.

(b) Write a balanced chemical equation, including state symbols, for the reaction of hydrochloric acid with solid copper(II) oxide.

(c) Write a balanced chemical equation, including state symbols, for the reaction of hydrochloric acid with aqueous potassium hydroxide.

(d) (i) The reaction with magnesium ribbon is the only one of the four that does not produce water. Identify the gaseous product of this reaction.

(d) (ii) Write the balanced chemical equation, including state symbols, for the reaction between magnesium and hydrochloric acid.

(e) State the type of reaction that occurs between hydrochloric acid and potassium hydroxide.

A nitrogenous base, compound Y, extracted from a plant species, was found to have the following percentage composition by mass:

C = 60.94%

H = 15.37%

N = 23.69%

(a) Determine the empirical formula of compound Y.

(b) A solution was prepared by dissolving 1.18 g of Y in deionized water to make a 50.00 cm³ solution. A 25.00 cm³ aliquot of this solution was titrated with 0.500 mol dm⁻³ hydrochloric acid, HCl(aq). Complete neutralization required 20.00 cm³ of the HCl solution. Determine the molar mass (M) of Y.

(c) State the molecular formula of Y.

(d) Compound Y is a weak base that reacts with water according to the equation:

Y(aq) + H₂O(l) ⇌ YH⁺(aq) + OH⁻(aq)

Identify the functional group present in Y.

Nitrogen dioxide, a pollutant from car exhausts, reacts with water in the atmosphere to form nitric acid and nitrous acid. This is a disproportionation reaction.

$2NO_{2}(g) + H_{2}O(l) \rightleftharpoons HNO_{3}(aq) + HNO_{2}(aq)$

(a) Deduce the oxidation states of nitrogen in the reactant and products.

Reactant: $NO_{2}$

Products: $HNO_{3}$, $HNO_{2}$

(b) Explain, with reference to the equilibrium, why more nitrogen dioxide gas dissolves when the reaction occurs in alkaline rainwater.

(c) The solubility of nitrogen dioxide gas in water was measured by different scientific groups. A summary of their results is shown.

(i) Identify a problem in comparing the data from the different sources as presented in the table.

(ii) The units of solubility are converted to mol dm⁻³. Complete the table by calculating the value for source A. Assume the atmospheric pressure is 100 kPa and the density of the resulting solution is 1.00 g cm⁻³.

(iii) Suggest an explanation for the effect of temperature on the solubility of nitrogen dioxide gas.

(d) Suggest one reason why nitrogen dioxide is considered a major air pollutant.

(e) Nitrous acid, $HNO_2$, is a weak acid. The graph shows the percentage of nitrous acid and its conjugate base, the nitrite ion ($NO_2^-$), present at different pH values.

(GRAPH IS A STANDARD SPECIATION PLOT FOR A WEAK ACID. X-AXIS: pH from 0 to 8. Y-AXIS: Percentage from 0 to 100. A curve for HA starts at 100% and goes down, a curve for A- starts at 0% and goes up. The two curves cross at pH = 3.3, where each is at 50%.)

(i) Deduce the pH range where nitrous acid, $HNO_{2}$, is the dominant nitrogen-containing species in the solution.

(ii) Determine, with reference to the graph, the $pK_a$ of nitrous acid.

(f) Nitrous acid can react with secondary amines to form N-nitrosamines, which are potent carcinogens. An example is the reaction with dimethylamine, $(CH_3)_2NH$.

(i) Deduce a balanced chemical equation for the formation of N-nitrosodimethylamine, $(CH_3)_2NNO$, from dimethylamine and nitrous acid.

(ii) The rate of N-nitrosamine formation is highly dependent on pH. The reaction rate is highest under mildly acidic conditions where there is a sufficient concentration of both the unprotonated amine and nitrous acid. State two conditions that could be maintained in an industrial process to minimize the formation of N-nitrosamines.

(g) To combat the effects of acid rain, powdered limestone ($CaCO_3$) is sometimes added to lakes. Suggest two distinct reasons why this 'liming' process is effective at restoring the aquatic ecosystem.

An experiment was conducted to investigate the effect of temperature on the rate of reaction between excess calcium carbonate chips and 100 cm³ of 0.5 mol dm⁻³ hydrochloric acid. The volume of carbon dioxide gas produced was collected in a gas syringe. The results for the reaction at 25 °C (Experiment 1), 35 °C (Experiment 2), and 45 °C (Experiment 3) are plotted on the graph below.

(a) By annotating the graph, determine the initial rate of reaction for Experiment 2, in cm³ s⁻¹.

(b) Estimate the time required for Experiment 1 to produce half of the total volume of CO₂.

(c) Suggest two reasons, in terms of collision theory, why the rate of reaction in Experiment 3 (45 °C) is greater than in Experiment 1 (25 °C).

(d) Calculate the percentage increase in the volume of CO₂ produced after 20 seconds when the temperature is increased from 25 °C (Experiment 1) to 45 °C (Experiment 3).

(e) The experiment was performed in a sealed flask connected to the gas syringe. Sketch a graph of the total mass of the apparatus against time for Experiment 1 and provide a reason for its shape.

Antimony (Sb) and Bismuth (Bi) are elements in group 15 of the periodic table.

(a) Antimony has two stable isotopes. 57.21% of antimony atoms contain 70 neutrons and the remainder contain 72 neutrons.

(i) Deduce the nuclear symbol of the isotope of antimony containing 72 neutrons. Use section 6 of the data booklet.

(ii) Calculate, to two decimal places, the relative atomic mass of antimony.

Bismuth(III) nitrate, $Bi(NO_3)_3$, is a common salt of bismuth.

(b) (i) The compound contains both ionic and covalent bonds. State which particles are joined by covalent bonds and which are joined by ionic bonds.

(ii) Distinguish between covalent and ionic bonding in terms of electron distribution.

(iii) State the enthalpy term that characterizes the strength of the bonding between the ions in an ionic solid.

(iv) Write an equation for the formation of aqueous bismuth(III) nitrate from solid bismuth(III) oxide and nitric acid.

(v) Calculate the volume, in $cm^3$, of $1.50 \text{ mol dm}^{-3}$ nitric acid required to react completely with $5.00 \text{ g}$ of solid bismuth(III) oxide.

(vi) Predict, with a reason, whether bismuth(III) oxide is expected to be primarily acidic, basic or amphoteric.

(vii) Discuss how the relative reactivity of zinc and bismuth could be established using the metals and aqueous solutions of their nitrates.

(viii) Discuss the products formed at the electrodes during the electrolysis of aqueous bismuth(III) nitrate. Use the standard electrode potential $E^\ominus(Bi^{3+}/Bi) = +0.32 \text{ V}$ and section 24 of the data booklet.

Bismuth compounds are sometimes used in fireworks to produce special effects.

(c) (i) State the feature of the atomic emission spectrum of an element that corresponds to its first ionization energy.

(ii) Calculate the wavelength, in nm, that corresponds to the first ionization energy of bismuth. Use sections 1, 2 and 8 of the data booklet.

(iii) Explain why the first ionization energy of bismuth is lower than that of polonium (Po), in terms of nuclear charge and electron shielding.

A student investigates the rate of reaction between magnesium and sulfuric acid. The reaction produces hydrogen gas.

(a) Write the balanced chemical equation, including state symbols, for the reaction between magnesium and sulfuric acid.

(b) Describe two different experimental methods to measure the rate of this reaction. For each method, state the variable that would be measured.

The student carries out the reaction using 0.50 g of magnesium and excess 1.0 mol dm⁻³ sulfuric acid. The experiment is performed twice: once with a single ribbon of magnesium and once with the same mass of magnesium powder. The results are plotted on the graph below.

(c) (i) Identify which curve, A or B, represents the reaction with magnesium powder. Explain your answer using collision theory.

(ii) Explain why both curves reach the same final volume of hydrogen gas.

A sample of chlorine consists of two isotopes, $^{35}Cl$ and $^{37}Cl$.

(a) Contrast the sub-atomic structure of these two isotopes.

(b) (i) The sample of chlorine is analysed in a mass spectrometer, producing a spectrum for the $Cl_2^+$ ion. The spectrum shows three peaks at m/z values of 70, 72 and 74. Explain the origin and relative heights of these three peaks, given that the abundance of $^{35}Cl$ is approximately three times that of $^{37}Cl$.

(ii) A more precise measurement finds the composition by mass to be: $^{35}Cl$: 75.76%, $^{37}Cl$: 24.24%. Calculate the relative atomic mass of chlorine from this sample, giving your answer to two decimal places. (Use isotopic masses of 35.0 and 37.0 for this calculation).

Magnesium chloride, $MgCl_2$, and manganese(II) chloride, $MnCl_2$, are two ionic compounds.

(c) (i) Deduce the type of bonding in magnesium chloride, $MgCl_2$, using electronegativity values from section 9 of the data booklet.

(ii) Determine the lattice enthalpy of magnesium chloride, assuming the bonding is purely ionic. Use sections 9, 10 and 12 of the data booklet and the following data:

Enthalpy of formation of magnesium chloride = $-641 \text{ kJ mol}^{-1}$

(iii) Explain, with reference to electron configurations, why the ionic radii of $Mg^{2+}$, $Mn^{2+}$ and $Cl^-$ are different. Use section 10 of the data booklet.

(iv) Predict, with a reason, which has the stronger ionic bonding, manganese(II) chloride, $MnCl_2$, or magnesium chloride.

Magnesium chloride is white, but manganese(II) chloride is pale pink.

(d) (i) State the condensed electron configuration of a manganese atom.

(ii) State the reason, in terms of electron configuration, why manganese(II) chloride is coloured.

(iii) Manganese(II) chloride absorbs light with a wavelength of approximately 530 nm. Describe why this is consistent with the observed colour of the compound. Use sections 2 and 15 of the data booklet.

A copper key is to be electroplated with manganese using an aqueous solution of manganese(II) chloride as the electrolyte.

(e) (i) Deduce the half-equations for the reactions occurring at the anode (made of pure manganese) and the cathode (the copper key).

(ii) Deduce a balanced chemical equation for the reaction of fluorine gas with the aqueous chloride ions in the electrolyte.

Strontium is an alkaline earth metal in group 2 of the periodic table, used to produce the red colour in fireworks.

(a) In a sample of strontium, 10.0% of the atoms have a mass number of 86 and the remainder have a mass number of 88.

(i) Deduce the nuclear symbol of the isotope of strontium with mass number 86. Use section 6 of the data booklet.

(ii) Calculate, to two decimal places, the relative atomic mass of this sample of strontium.

(iii) Explain why the first ionization energy of strontium is greater than that of rubidium.

(b) Strontium nitrate has the formula $Sr(NO_3)_2$.

(i) The compound contains both ionic and covalent bonds. State which particles are joined by covalent bonds and which are joined by ionic bonds.

(ii) Contrast covalent and ionic bonds in terms of how the valence electrons are involved.

(iii) Write a balanced chemical equation for the formation of strontium nitrate solution from the reaction of solid strontium hydroxide with nitric acid.

(iv) Calculate the volume, in $cm^3$, of $1.50 \text{ mol dm}^{-3}$ nitric acid required to react completely with $5.00 \text{ g}$ of solid strontium hydroxide.

(v) Predict, with a reason, whether strontium oxide is acidic, basic or amphoteric.

(vi) Describe an experiment to establish the relative reactivity of strontium and zinc using the metals and aqueous solutions of their nitrates.