Calculating Rate from Numerical Data

• Reactions take place at different rates depending on the identities and conditions.
• Some are extremely slow e.g. rusting and others are extremely fast e.g. explosives.
• Rates of reaction can be measured either by how fast a reactant is used up or by how fast the product is made.
• Rate is concerned with amounts of substances and time and can be calculated using the formula:

• Several measurements need to be made during the reaction which makes determining the reaction rate a technically difficult procedure.
• The product is usually the one that is measured as practically it is easier to measure a product forming than it is a reactant disappearing.
• The quantity to be measured depends on the reaction and may be in grams for mass or cm3 or dm3 for volume if the product is a gas.
• The units of the rate of reaction would therefore be g s-1 or cm3 / dm3 s-1, which can then be converted into mol dm3 s-1.
• Time is usually in seconds as most reactions naturally occur fast.
• If one of the products is a gas which is given off, then the reaction can be performed in an open flask on a balance to measure the loss in mass of reactant.
• Cotton wool is usually placed in the mouth of the flask which allows gas out but prevents any materials from being ejected from the flask (if the reaction is vigorous).

Diagram showing the set-up to measure the rate of reaction by loss of mass (gas)

• This method is not suitable for hydrogen and other gases with a small relative formula mass, Mr as the loss in mass may be too small to measure.
• Alternatively the gas could be captured in a gas syringe which measures its volume.

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Diagram of a gas syringe used to determine the rate of reaction

• Precipitation reactions form a solid precipitate when two clear solutions are mixed together.
• The precipitate clouds the reaction mixture so if the flask is placed over a piece of paper with a cross on it, the time it takes for the cross to disappear from view (due to the formation of the precipitate) can be measured.

Diagram showing rate study of a precipitation reaction

• The same technique can be employed if the reactants are coloured or turbid and the product is transparent.
• This method is susceptible to error though as they are subjective, given that different people may not agree on the exact moment that the cross disappears.
• Another disadvantage is that only one data point is produced per experiment, so a rate of reaction graph cannot be plotted.

Drawing & Interpreting Rate Graphs

• Data recorded in rate studies are used to plot graphs to calculate the rate of a reaction.
• Time is normally plotted on the x-axis with the concentration of the reactant or product on the y-axis.
• A number of measurements should be taken to provide a complete set of data.
• If the relationship between the factor being measured and the amount produced is directly proportional (i.e. if the concentration of a reactant doubles the rate also doubles) then the resulting graph will be a straight line graph going through the origin.
• The gradient of the line is equal to the rate of reaction and the steeper the gradient of the line then the faster the rate of reaction.
• Over time the rate of reaction slows as the reactants are being used up so the line becomes less steep and eventually becomes horizontal, indicating the reaction has finished.
• The gradient of a straight line is given by the equation:

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• You can also tell just by looking at a graph whether the data was produced from measuring the reactant being used up or the product forming.
• A reaction rate graph based on measurements of a product being formed will have a positive correlation.

Rate Graphs of Products Formed

• Initial amount of product is 0.
• Positive correlation of the graph indicates the amount of product increases as the reaction progresses.
• A reaction rate graph based on measurements of a reactant being used up will have a negative correlation.
Rate Graphs of Reactant Used
• Initial amount of reactant is at its maximum value.
• Negative correlation of the graph indicates the amount of reactant decreases as the reaction progresses.
• If the amounts of reactants are adjusted or if the concentration or pressure are changed, then the corresponding reaction graphs will also be different.

Mass / Volume

Graph showing the effect of mass / volume on the rate of reaction

• Compared to a reaction with less mass / volume of reactant, the graph for the same reaction with a higher mass / volume has a steeper gradient at the start and becomes horizontal sooner.
• This shows that with increased mass / volume of a reactant, the rate of reaction increases as does the amount of product formed.

Concentration / Pressure

Graph showing the effect of concentration of a solution on the rate of reaction

• Compared to a reaction with low concentration / pressure, the graph for the same reaction at a higher concentration / pressure has a steeper gradient at the start and becomes horizontal sooner.
• This shows that with increased concentration / pressure of a reactant, the rate of reaction increases.

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Author: Morgan

Morgan’s passion for the Periodic Table begun on his 10th birthday when he received his first Chemistry set. After studying the subject at university he went on to become a fully fledged Chemistry teacher, and now works in an international school in Madrid! In his spare time he helps create our fantastic resources to help you ace your exams.