6.1.1a Calculating rates of reactions
Rate of reaction measures how quickly reactants turn into products
Definition
Rate of reaction
The change in the quantity of a reactant used or a product formed per unit time.
Definition
Reactant
A reactant is a substance that is changed or used up during a chemical reaction.
- The rate of reaction tells you how quickly a reactant is used up or a product is made.
- You can follow the rate by measuring either a reactant being used up or a product being formed.
- The mean rate is the average rate over a chosen time.
- Find it from mean rate=quantity of reactant used or product formedtime taken\text{mean rate} = \dfrac{\text{quantity of reactant used or product formed}}{\text{time taken}}mean rate=time takenquantity of reactant used or product formed.
- The unit depends on what you measured: mass gives g/s\text{g/s}g/s, gas volume gives cm3/s\text{cm}^3\text{/s}cm3/s and amount gives mol/s\text{mol/s}mol/s.
Key Idea
- Rate is a change in quantity divided by the time taken for that change.
- Following the reactant or the product gives the same reaction rate.
Follow a rate by mass loss, gas volume or cloudiness
Definition
Product
A product is a substance formed during a chemical reaction.
- Mass loss: stand the flask on a balance and record the falling mass as a gas escapes.
- Gas volume: collect the gas in a gas syringe or an upturned measuring cylinder and record its volume.
- Cloudiness: time how long a reaction takes to hide a mark placed under the flask.
- Which method you choose depends on whether the reaction gives off a gas or forms a cloudy solid.
Example
- A reaction gives off 24 cm324\ \text{cm}^324 cm3 of gas in 40 s40\ \text{s}40 s.
- The mean rate is 2440=0.6 cm3/s\dfrac{24}{40} = 0.6\ \text{cm}^3\text{/s}4024=0.6 cm3/s.
Read a mean rate straight from the numbers, keeping the units
- Take the quantity at the start and at the end of the time you are interested in.
- Subtract to find the change in quantity, then divide by the time taken.
- Write the unit that matches the measurement, such as cm3/s\text{cm}^3\text{/s}cm3/s or g/s\text{g/s}g/s.
- A mean rate is an average, so it does not show that the reaction is fastest at the start.
Exam technique
- Show the change in quantity and the time as a fraction, then divide, so the method is clear.
- Always give the unit; a rate with no unit usually loses a mark.
- Read values carefully from a graph or table before you subtract.
Self review
- What does the rate of a reaction tell you?
- Write the equation for the mean rate of a reaction.
- Give two quantities you could measure to follow a reaction that gives off a gas.
- A reaction forms 36 cm336\ \text{cm}^336 cm3 of gas in 30 s30\ \text{s}30 s; what is the mean rate?
6.1.1b Gradient of a tangent as rate
A rate graph plots the amount of product or reactant against time
Definition
Rate of reaction
The change in the quantity of a reactant used or a product formed per unit time.
- Plot the quantity measured, such as gas volume, on the vertical axis and time on the horizontal axis.
- The line is steepest at the start, because the reaction is fastest when the most reactant is present.
- The line gradually becomes less steep as the reactants are used up.
- The line becomes flat when the reaction has finished and no more product forms.
- A reaction that finishes sooner, with a steeper line, is the faster reaction.
Key Idea
- The steeper the line, the faster the reaction at that moment.
- A flat line means the reaction has stopped.
The gradient of the line gives the rate at that time
Definition
Gradient
The change in the vertical-axis value divided by the corresponding change in the horizontal-axis value.
- The gradient is the change on the vertical axis divided by the change on the horizontal axis.
- A steeper gradient means a faster rate.
- For a straight part of the line, pick two points and divide the change in quantity by the change in time.
For a curve, draw a tangent and use its gradient
Definition
Tangent
A straight line drawn at a chosen point on a curve with the same gradient as the curve at that point.
- On a curve the rate is always changing, so you cannot read it from the curve directly.
- Draw a tangent that just touches the curve at the time you are interested in.
- Make the tangent as long as you can, because a longer line gives a more accurate gradient.
- Read the change in quantity and the change in time along the tangent.
- The gradient of the tangent is the rate of reaction at that instant.
Example
- A tangent drawn at 20 s20\ \text{s}20 s rises by 30 cm330\ \text{cm}^330 cm3 over 20 s20\ \text{s}20 s of the graph.
- The rate at that moment is 3020=1.5 cm3/s\dfrac{30}{20} = 1.5\ \text{cm}^3\text{/s}2030=1.5 cm3/s.
Common Mistake
- Draw the tangent so it touches the curve at one point, not so it cuts across it.
- Use a large triangle on the tangent, because a small one makes the gradient less accurate.
Exam technique
- For an overall rate, use the whole change and the total time; for the rate at a moment, use a tangent.
- Mark the triangle you used on the graph so the examiner can follow your gradient.
- Give the unit of the rate, matching the axis you measured.
Self review
- Why is a rate graph steepest at the start?
- What does a flat section of the line show?
- How do you find the rate at a particular time from a curved graph?
- Why should a tangent be drawn as long as possible?
