1.9.2 Calculating Rates of Reaction

• To measure the rate of a reaction, we need to be able to measure either how quickly the reactants are used up or how quickly the products are formed
• The method used for measuring depends on the substances involved
• There are a number of ways to measure a reaction rate in the lab; they all depend on some property that changes during the course of the reaction
• That property is taken to be proportional to the concentration of the reactant or product, e.g., colour, mass, volume
• Some reaction rates can be measured as the reaction proceeds (this generates more data);
  • faster reactions can be easier to measure when the reaction is over, by averaging a collected measurement over the course of the reaction

• Commonly used techniques are:
  • mass loss
  • gas production

Changes in mass

• When a gas is produced in a reaction it usually escapes from the reaction vessel, so the mass decreases
  • This can be used to measure the rate of reaction
  • For example, the reaction of calcium carbonate with hydrochloric acid produces CO₂
  • The mass is measured every few seconds and change in mass over time is plotted as the CO₂ escapes

Measuring changes in mass using a balance

• The mass loss provides a measure of the amount of reactant, so the graph is the same as a graph of amount of reactant against time

Mass loss of a product against time

• However, one limitation of this method is the gas must be sufficiently dense or the change in mass is too small to measure on a 2 or 3 d.p. balance
  • So carbon dioxide would be suitable (M_r = 44.0) but hydrogen would not (M_r = 2.0)

Volumes of gases

• When a gas is produced in a reaction, it can be trapped and its volume measured over time
  • This can be used to measure the rate of reaction.
  • For example, the reaction of magnesium with hydrochloric acid produces hydrogen

Collecting gases experimental set up

• An alternative gas collection set up involves collecting a gas through water using an inverted measuring cylinder (as long as the gas is not water soluble)

Alternative gas collection set up

• The volume can be measured every few seconds and plotted to show how the volume of gas varies with time
• The volume provides a measure of the amount of product, so the graph is a graph of amount of product against time

 Graph of gas volume evolved against time

Measuring concentration changes

• Measuring concentration changes during a reaction is not easy; the act of taking a sample and analysing it by titration can affect the rate of reaction (unless the reaction is deliberately stopped- this is called quenching).
• Often it is more convenient to ‘stop the clock’ when a specific (visible) point in the reaction is reached
  • For example when a piece of magnesium dissolves completely in hydrochloric acid
  • Another common rate experiment is the reaction between sodium thiosulfate and hydrochloric acid which slowly produces a yellow precipitate of sulfur that obscures a cross when viewed through the solution:

Na₂S₂O₃ (aq) + 2HCl (aq)   →  2NaCl aq) + SO₂ (g) + H₂O (l) + S(s)

The disappearing cross experiment

• The main limitation here is that often it only generates one piece of data for analysis

Answer

Step 1: Draw a graph of the results

• • The gradient can be used to give the rate of reaction, however, the graph has produced a curve

Step 2: Draw a tangent to the curve at time = 0 seconds

Step 3: Calculate the gradient 

• • Gradient 1.05 mol dm^-3 s^-1