1.3 The Mole, Avogadro & The Ideal Gas Equation

A student performs a titration to determine the molar mass and structure of a weak acid, X, which contains C, H and O only. One molecule of X contains two COOH groups.

The student prepares a 250.0 cm³ solution from 1.513 g of X. The solution of X is added to the burette and titrated with 25.0 cm³ aliquot of 0.112 mol dm^-3 NaOH (aq). 

1 mol of X reacts with 2 mol of NaOH.

The student obtains a mean titre of 27.30 cm³.

Calculate the molar mass of X.

Suggest a structure for X.

Ethanedioic acid (H₂C₂O₄) is a naturally occuring diprotic acid and can be used to bleach and restore wood.

A student carried out a titration with sodium hydroxide solution to determine the mass of the acid in the solution. 

H₂C₂O₄ (aq) + 2NaOH (aq)  ⟶  Na₂C₂O₄ (aq) + 2H₂O (l)

After achieving concordant results, the student found that 26.0 cm³ of the ethanedioic acid solution reacted completely with 26.40 cm³ of 0.600 mol dm⁻³ sodium hydroxide solution.

A student wanted to investigate Dalton’s Law, which states that in a mixture of non reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. The student connected two flasks of different sizes, C and D, via a stopcock as shown in Figure 1. 

Flask D contains methane, which occupies a volume of 1500 cm³. The tap is closed and there is a vacuum in flask C.

The conditions of flask D are 105 kPa and 320 K.

The gas constant R = 8.31 J K⁻¹ mol⁻¹

Barium in group 2 of the periodic table, reacts with oxygen to form barium oxide, an ionic compound which can be used as a drying agent. 

Calculate the number of barium ions in 1.75 g of barium oxide.

Give your answer in standard form and to three significant figures.

Selenium is in the same group of the periodic table as sulfur. Sodium selenide reacts with hydrochloric acid to form a toxic gas, A, with a relative molecular mass of 81.0 and sodium chloride.

The organic compound cyclohexene can be synthesised from bromocyclohexane in a two step process involving an intermediate species E and specific reaction conditions and reagents, as shown in Figure 1.

A student carries out this synthesis and obtains 1.36 g of pure cyclohexene from 5.75 g of bromocyclohexane, from a 1:1 molar ratio of 1-bromocyclohexane to cyclohexene.

Calculate the percentage yield of cyclohexene.

Give your final answer to an appropriate number of significant figures.

Alcohol X contains carbon, hydrogen and oxygen only. The alcohol is a liquid at room temperature and pressure but can easily be vaporised.

1.15 g of X produces 761 cm³ of gas when vaporised, measured at 100 kPa and 366 K.

Borax, Na₂B₄O₇.10H₂O, can be used to determine the concentration of acids such as dilute hydrochloric acid. A student prepares 250 cm³ of a 0.0800 mol dm^-3 solution of borax in water in a volumetric flask.

Calculate the mass of borax crystals, Na₂B₄O₇.10H₂O, needed to make up 250 cm³ of 0.0800 mol dm^-3 solution. 

Give your answer to three significant figures.

A student performed an experiment and dissolved 1.85 g of a metal carbonate, M₂CO₃, into distilled water to make 250 cm³ of solution. A 25.0 cm³ portion of the solution required 17.4 cm³ of 0.200 mol dm^-3 hydrochloric acid for a complete reaction.

M₂CO₃ (aq) + 2HCl (aq) → 2MCl (aq) + CO₂ (g) + H₂O (l)

Deduce the relative atomic mass and identity of metal M.

In an experiment to determine the quantity of iodide in a sample of dried seaweed, 60.0 g of seaweed was treated in water and the released iodide ions were made up to 250 cm³ in a volumetric flask. 25.0 cm³ of the solution was removed, an indicator added and the solution was found to react with 22.35 cm³ of 0.0100 mol dm^-3 potassium dichromate. The ionic equation for the reaction is shown below.

Cr₂O₇^2- + 14H⁺ + 6I^- → 3I₂ + 2Cr³⁺ + 7H₂O

Calculate the percentage mass of iodine in the seaweed.

The compound 2-phenylethyl propanoate is a synthetic oil used in some fragrances due to its rose-like aroma. 1.56 g of 2-phenylethyl propanoate was combusted in oxygen and produced 4.26 g of CO₂ and 1.1 g of H₂O.

Explain how the results above support the molecular formula of 2-phenylethyl propanoate, C₁₁H₁₄O₂.

Boron and aluminium are in the same group of the Periodic Table. Both form compounds with chlorine and with fluorine.

Aluminium also reacts directly with chlorine to form a compound, aluminium chloride, containing only aluminium and chlorine. A 0.500 g sample of aluminium chloride was analysed and found to contain 0.101 g of aluminium. Another 0.500 g sample was heated to 473 K. The gas produced occupied a volume of 73.6 cm³ at a pressure of 1.00 × 10² kPa.

The gas constant R = 8.31 J K⁻¹ mol⁻¹ 

Calculate the molecular formula of the gas.

Phosphine, PH₃, is a gas formed by heating phosphorous acid, H₃PO₃, in the absence of air, as shown in the equation below.

4H₃PO₃ (s) → PH₃ (g) + 3H₃PO₄ (s)

3.45 ×10⁻² mol of H₃PO₃ is completely decomposed by this reaction.

Calculate the volume of phosphine gas formed, in cm³, at 100 kPa pressure and 210 °C.

When exposed to air, phosphine spontaneously ignites, forming P₄O₁₀ and water.

Construct an equation for this reaction. State symbols are not required.

Iron tablets are often taken to help reverse low iron levels in the blood. A student performed an experiment to determine the percentage mass of iron in iron tablets. 

They ground up iron tablets with a total mass of 5.90 g and dissolved them in excess, warm, dilute sulfuric (VI) acid and the solution was then made up to 500 cm³ in a volumetric flask. 25.0 cm³ of this solution was removed by pipette and titrated against 0.0500 mol dm^-3 of potassium manganate (VII) solution. The student needed 17.40 cm³ of potassium manganate to react with the iron solution. The ionic equation for the reaction is shown below.

MnO₄^- + 8H⁺ + 5Fe²⁺ → 5Fe³⁺ + Mn²⁺ + 4H₂O

Calculate the percentage mass of iron in the tablets dissolved in the original solution.

Calcium sulfate is a calcium salt which can be used as a food additive such as in flour. 

In a laboratory, a student wanted to make a precipitate of calcium sulfate by dissolving a 3.72 g sample of calcium chloride in water which reacted with an excess of sulfuric acid to form a precipitate of calcium sulfate. The percentage yield of calcium sulfate was 85.7%.

Europium reacts with dilute sulfuric acid, forming a solution of europium sulfate, Eu₂(SO₄)₃, and hydrogen gas. A chemist reacts 0.608 g of europium with an excess of H₂SO₄ (aq) and collects 144 cm³ of hydrogen gas at room temperature and pressure.

Using the chemists’ results, write the overall equation for the reaction between europium and sulfuric acid. State symbols are not required.

Show all of your working.

A group of students completed an experiment to calculate the M_r of a metal hydrogen carbonate, XHCO₃. 

First, the students made a stock solution of XHCO₃, by dissolving 1773 mg in a small amount of water, transferring it into a 250 cm³ volumetric flask and then making the solution up to the line of the flask. The students then took 20.0 cm³ samples of the solution and titrated them with 0.105 mol dm^-3 nitric acid.

Their results are recorded in Table 1. 

Table 1

Calculate the amount, in moles, of nitric acid that reacted with 20.0 cm³ of the XHCO₃ solution. 

Using your answer to part (a), calculate the amount in moles of XHCO₃ in the original 250 cm³ solution made by the students. 

Calculate a value for the Mr of XHCO3 and determine the identity of the metal, X. 

The burette used by the students for their titration has an error of ± 0.05 cm³. 

Suggest the maximum percentage uncertainty in using this piece of equipment. Use 14.50 cm³ as a mean titre for your calculation. Note, this is not the correct answer for the mean titre in part (a). 

Potassium chlorate (VII), KClO, decomposes to form potassium chloride and oxygen.

At 25℃ and 100 kPa, the oxygen gas produced occupied a volume of 1.08 × 10^–4 m³.

The gas constant R = 8.31 J K^-1 mol^-1

Calculate the number of moles of oxygen produced.

Whilst completing the reaction below, a chemist added excess calcium carbonate to 37.5 cm³ of 0.678 mol dm^-3 nitric acid. 

CaCO₃ (s) + 2HNO₃ (aq) → Ca(NO₃)₂ (aq) + H₂O (l) + CO₂ (g)

Calculate the minimum mass of calcium carbonate which would be needed to ensure that all of the nitric acid has reacted. 

Another common reaction of calcium carbonate is thermal decomposition. When heated, calcium carbonate decomposes according to the following equation:

CaCO₃ (s) → CaO (s) + CO₂ (g)

A 2.50 g sample of calcium carbonate was decomposed completely upon heating, at a temperature of 32.0 C and a pressure of 100 kPa. 

Calculate the volume of gas produced in cm³. 

The gas constant, R, is 8.31 JK^-1mol^-1. 

When hydrated, calcium carbonate can be represented using the formula CaCO₃.xH₂O. A 5.72 g sample of hydrated copper carbonate contains 2.97 g of water of crystallisation.

Calculate the value of x. 

A student was given homework to plan how to produce a standard solution in a volumetric flask, and then complete a simple titration experiment. 

The student came up with the following method for preparing the standard solution:

1. Collect all equipment
2. Use a pan balance to measure the amount of solid for the experiment. 
3. Tip the solid into a clean volumetric flask and rinse with distilled water to make sure all of the solid is in the flask. 
4. Make the solution up to 250 cm³ using distilled water. 
5. Add the lid, and shake well to make sure all of the solid is dissolved in the solution.
   

State four additional instructions which would improve the students’ overall method. These instructions could be placed at any stage of the method. 

The student then completes a titration to find the concentration of sulfuric acid. They found that 18.50 cm³ of sulfuric acid exactly neutralised 25.00 cm³ of 0.070 mol dm^-3 sodium hydroxide.

Write an equation for this reaction.

Calculate the concentration of the sulfuric acid, in mol dm^-3.

Once the titration was complete, the student left the collected solution and crystals began to form. The formula of the crystals formed is NaSO₄.xH₂O

What name is given to the .xH₂O part of the formula?

When magnesium reacts with hydrochloric acid, the following reaction occurs:

Mg (s) + 2HCl (aq) → MgCl₂ (aq) + H₂ (g)  

During the reaction, the hydrogen produced occupies 103 cm³ at 25.0 C and 100 kPa. 

Calculate the amount, in moles, of hydrogen gas produced during the reaction. 

The gas constant, R, is 8.31 J K^-1 mol^-1. 

Using your answer to part (a), calculate the exact volume in cm³ of 0.15 mol dm^-3 HCl, which would be needed to produce that amount of hydrogen gas.
Give your answer to 1 decimal place.

A student completed the same reaction as in part (a), using 3.75 g of magnesium. 

Calculate the mass of magnesium chloride produced by the student during this reaction.

Calculate the number of atoms of hydrogen produced during the students reaction in part (c).

The Avogadro constant, L = 6.022 x 10²³.