0.9 Quantitative aspects of chemical change

Stoichiometry

1. Diborane, $\mathrm{B}{}_2\mathrm{H}{}_6$ , was once considered for use as a rocket fuel. The combustion reaction for diborane is: ${\mathrm{B}}_2{\mathrm{H}}_6\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2\mathrm{H}\mathrm{B}{\mathrm{O}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ If we react $\mathrm{2,37}\mathrm{grams}$ of diborane, how many grams of water would we expect to produce?
   
2. Sodium azide is a commonly used compound in airbags. When triggered, it has the following reaction: $2{\mathrm{NaN}}_3\left(\mathrm{s}\right)\to 2\mathrm{Na}\left(\mathrm{s}\right)+3{\mathrm{N}}_2\left(\mathrm{g}\right)$ If $\mathrm{23,4}\mathrm{grams}$ of sodium azide is used, how many moles of nitrogen gas would we expect to produce?
   
3. Photosynthesis is a chemical reaction that is vital to the existence of life on Earth. During photosynthesis, plants and bacteria convert carbon dioxide gas, liquid water, and light into glucose ( $\mathrm{C}{}_6\mathrm{H}{}_{12}\mathrm{O}{}_6$ ) and oxygen gas.
   1. Write down the equation for the photosynthesis reaction.
   2. Balance the equation.
   3. If $3\mathrm{moles}$ of carbon dioxide are used up in the photosynthesis reaction, what mass of glucose will be produced?

Summary

• It is important to be able to quantify the changes that take place during a chemical reaction.
• The mole (n) is a SI unit that is used to describe an amount of substance that contains the same number of particles as there are atoms in $12\mathrm{g}$ of carbon.
• The number of particles in a mole is called the Avogadro constant and its value is $6,022\times {10}^{23}$ . These particles could be atoms, molecules or other particle units, depending on the substance.
• The molar mass (M) is the mass of one mole of a substance and is measured in grams per mole or $\mathrm{g}·\mathrm{mol}{}^{-1}$ . The numerical value of an element's molar mass is the same as its relative atomic mass. For a compound, the molar mass has the same numerical value as the molecular mass of that compound.
• The relationship between moles (n), mass in grams (m) and molar mass (M) is defined by the following equation:
  $$n=\frac{m}{M}$$
• In a balanced chemical equation, the number in front of the chemical symbols describes the mole ratio of the reactants and products.
• The empirical formula of a compound is an expression of the relative number of each type of atom in the compound.
• The molecular formula of a compound describes the actual number of atoms of each element in a molecule of the compound.
• The formula of a substance can be used to calculate the percentage by mass that each element contributes to the compound.
• The percentage composition of a substance can be used to deduce its chemical formula.
• One mole of gas occupies a volume of $\mathrm{22,4}{\mathrm{dm}}^3$ .
• The concentration of a solution can be calculated using the following equation,
  $$C=\frac{n}{V}$$
  where C is the concentration (in $\mathrm{mol}·{\mathrm{dm}}^{-3}$ ), n is the number of moles of solute dissolved in the solution and V is the volume of the solution (in ${\mathrm{dm}}^{-3}$ ).
• Molarity is a measure of the concentration of a solution, and its units are $\mathrm{mol}·{\mathrm{dm}}^{-3}$ .
• Stoichiometry is the calculation of the quantities of reactants and products in chemical reactions. It is also the numerical relationship between reactants and products.
• The theoretical yield of a reaction is the maximum amount of product that we expect to get out of a reaction

End of chapter exercises

1. Write only the word/term for each of the following descriptions:
   1. the mass of one mole of a substance
   2. the number of particles in one mole of a substance
2. Multiple choice: Choose the one correct answer from those given.
   1. $5\mathrm{g}$ of magnesium chloride is formed as the product of a chemical reaction. Select the true statement from the answers below:
      1. 0.08 moles of magnesium chloride are formed in the reaction
      2. the number of atoms of $\mathrm{Cl}$ in the product is $0,6022\times {10}^{23}$
      3. the number of atoms of $\mathrm{Mg}$ is 0,05
      4. the atomic ratio of $\mathrm{Mg}$ atoms to $\mathrm{Cl}$ atoms in the product is 1:1
   2. 2 moles of oxygen gas react with hydrogen. What is the mass of oxygen in the reactants?
      1. 32 g
      2. 0,125 g
      3. 64 g
      4. 0,063 g
   3. In the compound potassium sulphate ( $\mathrm{K}{}_2\mathrm{SO}{}_4$ ), oxygen makes up x% of the mass of the compound. x = ...
      1. 36.8
      2. 9,2
      3. 4
      4. 18,3
   4. The molarity of a $150{\mathrm{cm}}^3$ solution, containing 5 g of $\mathrm{NaCl}$ is...
      1. $\mathrm{0,09}\mathrm{M}$
      2. $\mathrm{5,7}\times 10{}^{-4}\mathrm{M}$
      3. $\mathrm{0,57}\mathrm{M}$
      4. $\mathrm{0,03}\mathrm{M}$
3. Calculate the number of moles in:
   1. 5 g of methane ( ${\mathrm{CH}}_4$ )
   2. 3,4 g of hydrochloric acid
   3. 6,2 g of potassium permanganate ( ${\mathrm{KMnO}}_4$ )
   4. 4 g of neon
   5. 9,6 kg of titanium tetrachloride ( ${\mathrm{TiCl}}_4$ )
4. Calculate the mass of:
   1. 0,2 mols of potassium hydroxide ( $\mathrm{KOH}$ )
   2. 0,47 mols of nitrogen dioxide
   3. 5,2 mols of helium
   4. 0,05 mols of copper (II) chloride ( ${\mathrm{CuCl}}_2$ )
   5. $\mathrm{31,31}\times {10}^{23}$ molecules of carbon monoxide ( $\mathrm{CO}$ )
5. Calculate the percentage that each element contributes to the overall mass of:
   1. Chloro-benzene ( ${\mathrm{C}}_6{\mathrm{H}}_5\mathrm{Cl}$ )
   2. Lithium hydroxide ( $\mathrm{LiOH}$ )
6. CFC's (chlorofluorocarbons) are one of the gases that contribute to the depletion of the ozone layer. A chemist analysed a CFC and found that it contained 58,64% chlorine, 31,43% fluorine and 9,93% carbon. What is the empirical formula?
   
7. 14 g of nitrogen combines with oxygen to form 46 g of a nitrogen oxide. Use this information to work out the formula of the oxide.
   
8. Iodine can exist as one of three oxides ( ${\mathrm{I}}_2{\mathrm{O}}_4;{\mathrm{I}}_2{\mathrm{O}}_5;{\mathrm{I}}_4{\mathrm{O}}_9$ ). A chemist has produced one of these oxides and wishes to know which one they have. If he started with 508 g of iodine and formed 652 g of the oxide, which form has he produced?
   
9. A fluorinated hydrocarbon (a hydrocarbon is a chemical compound containing hydrogen and carbon.) was analysed and found to contain 8,57% H, 51,05% C and 40,38% F.
   1. What is its empirical formula?
   2. What is the molecular formula if the molar mass is $\mathrm{94,1}\mathrm{g}\cdot {\mathrm{mol}}^{-1}$ ?
10. Copper sulphate crystals often include water. A chemist is trying to determine the number of moles of water in the copper sulphate crystals. She weighs out 3 g of copper sulphate and heats this. After heating, she finds that the mass is 1,9 g. What is the number of moles of water in the crystals? (Copper sulphate is represented by ${\mathrm{CuSO}}_4\cdot x{\mathrm{H}}_2\mathrm{O}$ ).
11. $300{\mathrm{cm}}^3$ of a $\mathrm{0,1}\mathrm{mol}·{\mathrm{dm}}^{-3}$ solution of sulphuric acid is added to $200{\mathrm{cm}}^3$ of a $\mathrm{0,5}\mathrm{mol}·{\mathrm{dm}}^{-3}$ solution of sodium hydroxide.
    1. Write down a balanced equation for the reaction which takes place when these two solutions are mixed.
    2. Calculate the number of moles of sulphuric acid which were added to the sodium hydroxide solution.
    3. Is the number of moles of sulphuric acid enough to fully neutralise the sodium hydroxide solution? Support your answer by showing all relevant calculations. (IEB Paper 2 2004)
12. A learner is asked to make $200{\mathrm{cm}}^3$ of sodium hydroxide ( $\mathrm{NaOH}$ ) solution of concentration $\mathrm{0,5}\mathrm{mol}·{\mathrm{dm}}^{-3}$ .
    1. Determine the mass of sodium hydroxide pellets he needs to use to do this.
    2. Using an accurate balance the learner accurately measures the correct mass of the $\mathrm{NaOH}$ pellets. To the pellets he now adds exactly $200{\mathrm{cm}}^3$ of pure water. Will his solution have the correct concentration? Explain your answer.
    3. The learner then takes $300{\mathrm{cm}}^3$ of a $\mathrm{0,1}\mathrm{mol}·{\mathrm{dm}}^{-3}$ solution of sulphuric acid ( $\mathrm{H}{}_2\mathrm{SO}{}_4$ ) and adds it to $200{\mathrm{cm}}^3$ of a $\mathrm{0,5}\mathrm{mol}·{\mathrm{dm}}^{-3}$ solution of $\mathrm{NaOH}$ at $25{}^0\mathrm{C}$ .
    4. Write down a balanced equation for the reaction which takes place when these two solutions are mixed.
    5. Calculate the number of moles of $\mathrm{H}{}_2\mathrm{SO}{}_4$ which were added to the NaOH solution.
    6. Is the number of moles of $\mathrm{H}{}_2\mathrm{SO}{}_4$ calculated in the previous question enough to fully neutralise the $\mathrm{NaOH}$ solution? Support your answer by showing all the relevant calculations. (IEB Paper 2, 2004)