6.1 Stoichiometry and composition  (Page 5/5)

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Sulfuric acid (H ${}_{2}$ SO ${}_{4}$ ) reacts with ammonia (NH ${}_{3}$ ) to produce the fertiliser ammonium sulfate ((NH ${}_{4}$ ) ${}_{2}$ SO ${}_{4}$ ) according to the following equation:

${H}_{2}S{O}_{4}\left(aq\right)+2N{H}_{3}\left(g\right)\to {\left(N{H}_{4}\right)}_{2}S{O}_{4}\left(aq\right)$

What is the maximum mass of ammonium sulphate that can be obtained from 2.0 kg of sulfuric acid and 1.0 kg of ammonia?

1. $n\left({H}_{2}S{O}_{4}\right)=\frac{m}{M}=\frac{2000g}{98.078g.mo{l}^{-1}}=20.39mol$
$n\left(N{H}_{3}\right)=\frac{1000g}{17.03g.mo{l}^{-1}}=58.72mol$
2. From the balanced chemical equation, 1 mole of H ${}_{2}$ SO ${}_{4}$ reacts with 2 moles of NH ${}_{3}$ to give 1 mole of (NH ${}_{4}$ ) ${}_{2}$ SO ${}_{4}$ . Therefore 20.39 moles of H ${}_{2}$ SO ${}_{4}$ need to react with 40.78 moles of NH ${}_{3}$ . In this example, NH ${}_{3}$ is in excess and H ${}_{2}$ SO ${}_{4}$ is the limiting reagent.

3. Again from the equation, the mole ratio of H ${}_{2}$ SO ${}_{4}$ in the reactants to (NH ${}_{4}$ ) ${}_{2}$ SO ${}_{4}$ in the product is 1:1. Therefore, 20.39 moles of H ${}_{2}$ SO ${}_{4}$ will produce 20.39 moles of (NH ${}_{4}$ ) ${}_{2}$ SO ${}_{4}$ .

The maximum mass of ammonium sulphate that can be produced is calculated as follows:

$m=n×M=20.41mol×132g.mo{l}^{-1}=2694g$

The maximum amount of ammonium sulphate that can be produced is 2.694 kg.

Stoichiometry

1. Diborane, B ${}_{2}$ H ${}_{6}$ , was once considered for use as a rocket fuel. The combustion reaction for diborane is: ${B}_{2}{H}_{6}\left(g\right)+3{O}_{2}\left(g\right)\to 2HB{O}_{2}\left(g\right)+2{H}_{2}O\left(l\right)$ If we react 2.37 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: $2Na{N}_{3}\left(s\right)\to 2Na\left(s\right)+3{N}_{2}\left(g\right)$ If 23.4 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 (C ${}_{6}$ H ${}_{12}$ O ${}_{6}$ ) and oxygen gas.
1. Write down the equation for the photosynthesis reaction.
2. Balance the equation.
3. If 3 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 g of carbon.
• The number of particles in a mole is called the Avogadro constant and its value is 6.023 $×$ 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 g.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 22.4 dm ${}^{3}$ .
• The concentration of a solution can be calculated using the following equation,
$C=\frac{n}{V}$
where C is the concentration (in mol.dm ${}^{-3}$ ), n is the number of moles of solute dissolved in the solution and V is the volume of the solution (in dm ${}^{3}$ ).
• Molarity is a measure of the concentration of a solution, and its units are mol.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.
• A limiting reagent is the chemical that is used up first in a reaction, and which therefore determines how far the reaction will go before it has to stop.
• An excess reagent is a chemical that is in greater quantity than the limiting reagent in the reaction. Once the reaction is complete, there will still be some of this chemical that has not been used up.

Summary exercise

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 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 Cl in the product is 0.6023 $×$ 10 ${}^{23}$
3. the number of atoms of Mg is 0.05
4. the atomic ratio of Mg atoms to 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 (K ${}_{2}$ 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 cm ${}^{3}$ solution, containing 5 g of NaCl is...
1. 0.09 M
2. 5.7 $×$ 10 ${}^{-4}$ M
3. 0.57 M
4. 0.03 M
3. 300 cm ${}^{3}$ of a 0.1 mol.dm ${}^{-3}$ solution of sulfuric acid is added to 200 cm ${}^{3}$ of a 0.5 mol.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 sulfuric acid which were added to the sodium hydroxide solution.
3. Is the number of moles of sulfuric acid enough to fully neutralise the sodium hydroxide solution? Support your answer by showing all relevant calculations. (IEB Paper 2 2004)
4. Ozone (O ${}_{3}$ ) reacts with nitrogen monoxide gas (NO) to produce NO ${}_{2}$ gas. The NO gas forms largely as a result of emissions from the exhausts of motor vehicles and from certain jet planes. The NO ${}_{2}$ gas also contributes to the brown smog (smoke and fog), which is seen over most urban areas. This gas is also harmful to humans, as it causes breathing (respiratory) problems. The following equation indicates the reaction between ozone and nitrogen monoxide: ${O}_{3}\left(g\right)+NO\left(g\right)\to {O}_{2}\left(g\right)+N{O}_{2}\left(g\right)$ In one such reaction 0.74 g of O ${}_{3}$ reacts with 0.67 g NO.
1. Calculate the number of moles of O ${}_{3}$ and of NO present at the start of the reaction.
2. Identify the limiting reagent in the reaction and justify your answer.
3. Calculate the mass of NO ${}_{2}$ produced from the reaction.
(DoE Exemplar Paper 2, 2007)
5. A learner is asked to make 200 cm ${}^{3}$ of sodium hydroxide (NaOH) solution of concentration 0.5 mol.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 NaOH pellets. To the pellets he now adds exactly 200 cm ${}^{3}$ of pure water. Will his solution have the correct concentration? Explain your answer.
3. The learner then takes 300 cm ${}^{3}$ of a 0.1 mol.dm ${}^{-3}$ solution of sulfuric acid (H ${}_{2}$ SO ${}_{4}$ ) and adds it to 200 cm ${}^{3}$ of a 0.5 mol.dm ${}^{-3}$ solution of NaOH at 25 ${}^{0}$ 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 H ${}_{2}$ SO ${}_{4}$ which were added to the NaOH solution.
6. Is the number of moles of H ${}_{2}$ SO ${}_{4}$ calculated in the previous question enough to fully neutralise the NaOH solution? Support your answer by showing all the relevant calculations. (IEB Paper 2, 2004)

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