Calculating rates of reactions — AQA GCSE Combined Science
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Calculating rates of reactions explained
Rate tells you how quickly a reaction proceeds.
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Measure it by tracking a reactant disappearing or a product appearing. For example, add marble chips to dilute hydrochloric acid and measure the carbon dioxide volume in a gas syringe every 10 s. The volume increases quickly at first, then slows as acid is used up. Alternatively, measure the decreasing mass of the flask as gas escapes. Plot quantity on the y-axis and time on the x-axis. The average rate over a time interval is the change in quantity divided by the time taken. For Higher Tier only, the gradient of a tangent at any point gives the rate at that specific moment; a steeper gradient means a faster reaction. Always record quantity and time together to calculate rate.
mean rate of reaction = quantity of reactant used / time taken
The mean rate of reaction is the average speed over a chosen time interval. Calculate it using: mean rate = quantity of reactant used ÷ time taken, or mean rate = quantity of product formed ÷ time taken. For example, if 2.4 g of reactant is used in 40 s, the mean rate is 2.4 g ÷ 40 s = 0.06 g/s. For a reactant, the quantity used is always the initial reading minus the final reading, regardless of when the interval starts. For a product, it is the final minus initial. Always include units: cm³/s, g/s, or mol/s (Higher Tier). A graph shows how rate varies; drawing a tangent allows finding the rate at a particular moment.
mean rate of reaction = quantity of product formed / time taken
The mean rate of reaction tells you how quickly a product appears, on average, across a chosen time interval. You calculate it by dividing the quantity of product formed by the time taken for that formation. The quantity may be a mass in grams or a volume in cm³, so the rate carries units such as g/s or cm³/s. For example, if 24 cm³ of gas is collected in 8 s, the mean rate is 24 cm³ ÷ 8 s = 3 cm³/s. The word mean signals an average over the interval, not the fastest or slowest moment. Choose two clear readings from the start and end of the interval, subtract to find the change in quantity, and divide by the time interval. Always give the unit and check that the time is in seconds before dividing.
The quantity of reactant or product can be measured by the mass in grams or by a volume in cm³.
To follow a reaction, you need a measurable quantity that changes as reactants are used up or products form. Mass in grams suits reactions that release a gas into the air, because the total mass falls as the gas escapes; a balance reading in g is recorded at timed intervals. Volume in cm³ suits reactions that produce a gas you can collect, for example in a gas syringe or over water; the volume is read at timed intervals. Either measurement can be plotted against time and used to find a rate. Choose the method that matches the reaction: if a gas is produced, volume or mass loss both work; if no gas forms, another property such as colour or pH may be needed. Record readings at regular times and keep other variables controlled.
The units of rate of reaction may be given as g/s or cm³/s.
Rate of reaction measures how quickly a reactant is used up or a product is formed. When the quantity is a mass, the rate is the mass change divided by the time taken, giving units of grams per second, g/s. When the quantity is a gas volume, the rate is the volume change divided by the time taken, giving units of cubic centimetres per second, cm³/s. For example, if 24 cm³ of gas is collected in 8 s, the mean rate is 24 cm³ ÷ 8 s = 3 cm³/s. If a reaction mixture loses 6.0 g in 30 s, the mean rate is 6.0 g ÷ 30 s = 0.20 g/s. The unit follows directly from the measured quantity, so choosing the right unit depends on what is being measured.
For the Higher Tier, students are also required to use quantity of reactants in terms of moles and units for rate of reaction in mol/s.
For Higher Tier students, the rate of reaction can be expressed using the amount of substance in moles. The amount in moles is calculated from mass and molar mass using the equation moles = mass ÷ molar mass. The rate is then the change in moles divided by the time taken, giving the unit mol/s. For example, if 0.50 mol of reactant is used in 25 s, the mean rate is 0.50 mol ÷ 25 s = 0.020 mol/s. This extends the foundation idea that rate is change divided by time: the change is now an amount in moles rather than a mass or a gas volume, so the unit becomes mol/s. Note that this specific calculation and unit apply only to Higher Tier assessments.
calculate the mean rate of a reaction from given information about the quantity of a reactant used or the quantity of a product formed and the time taken
To calculate the mean rate of a reaction, use the equation: mean rate = change in quantity ÷ time taken. The quantity may be a reactant used up or a product formed, measured in grams, cm³ of gas or moles. For example, if the mass of a reaction mixture falls from 50.0 g to 42.0 g in 20 s, the reactant used is 50.0 g − 42.0 g = 8.0 g, so the mean rate is 8.0 g ÷ 20 s = 0.40 g/s. If 15 cm³ of gas is produced in 30 s, the mean rate is 15 cm³ ÷ 30 s = 0.50 cm³/s. The word 'mean' means the average over the whole time interval, so it does not tell you the rate at a single instant. Always subtract the starting value if it is not zero, divide by the time, and give the correct unit.
draw, and interpret, graphs showing the quantity of product formed or quantity of reactant used up against time
When a reaction happens, the amount of product increases or the amount of reactant decreases as time passes. Plotting quantity on the y-axis against time on the x-axis gives a curve whose steepness shows how fast the reaction is going. A steep section means a fast reaction; a flat section means the reaction has stopped because a reactant has run out. For example, adding magnesium to dilute hydrochloric acid and collecting the hydrogen produced gives a curve that rises quickly then levels off. If you plot the mass of reactant remaining, the curve falls instead. However, a graph of 'reactant used up' will rise and level off, just like a product-formed graph. Always label both axes with quantity and unit, choose a sensible scale, plot points accurately and join them with a smooth curve.
draw tangents to the curves on these graphs and use the slope of the tangent as a measure of the rate of reaction
The rate of reaction at a particular moment relates to the slope of the quantity-time curve. Students draw a tangent: a straight line that touches the curve at the chosen time and follows its direction. The slope of this tangent is used as a measure of the rate of reaction; a steeper tangent indicates a faster rate. For example, a tangent drawn at 20 s that is steeper than one at 40 s shows the reaction is faster at 20 s. Tangents are most reliable where the curve is smooth. While all students must draw tangents and use the slope to compare rates, calculating the actual numerical gradient of the tangent is a Higher Tier only skill.
(HT only) calculate the gradient of a tangent to the curve on these graphs as a measure of rate of reaction at a specific time.
Rate graphs plot a quantity such as volume of gas or loss in mass against time. The gradient at any point equals the rate at that instant. Because the curve is not straight, you draw a tangent: a straight line touching the curve at the chosen time and matching its slope there. Pick two points far apart on the tangent, read their coordinates, then divide the change in y by the change in x. For example, if a tangent at 0 s passes through (0 s, 0 cm³) and (20 s, 40 cm³), the initial rate is 40 ÷ 20 = 2 cm³ s⁻¹. A steeper tangent means a faster reaction. Tangents can be drawn at the start (t=0) to find the initial rate. This calculation is higher-tier only.
Your focus
- Describe how to measure the rate of a reaction by following the loss of a reactant or the formation of a product over time.
- Calculate the average rate of a reaction over a stated time interval using the change in quantity and the time taken.
- Interpret a graph of quantity against time to determine the rate at a particular time from the gradient of a tangent (Higher Tier only).
Show all 30 objectives
- Calculate the mean rate of a reaction using the quantity of reactant used or product formed and the time taken.
- Use correct units for mean rate when the quantity is measured as volume, mass or amount in moles (Higher Tier only).
- Compare mean rates of different reactions or conditions using calculated values.
- Calculate the mean rate of reaction from a measured quantity of product and a measured time.
- Select the correct change in quantity and time interval from tabulated or graphical data.
- Express the mean rate with the correct compound unit.
- Describe how mass in grams can be used to follow a reaction that releases a gas.
- Describe how volume in cm³ can be used to follow a reaction that produces a gas.
- Choose and justify a suitable measurement method for a given reaction.
- Calculate the mean rate of a reaction from mass or gas volume data and give the unit as g/s or cm³/s.
- Select the appropriate unit for a rate of reaction by identifying whether mass or gas volume was measured.
- Explain why the unit of rate of reaction depends on the quantity measured and the time taken.
- Calculate the amount of reactant in moles and use it to determine a rate of reaction in mol/s.
- Convert mass data into moles using molar mass before calculating a rate.
- Apply the unit mol/s correctly when expressing a rate of reaction from mole data.
- Apply the equation mean rate = change in quantity ÷ time taken to data about a reactant used or a product formed.
- Calculate the change in quantity correctly when initial and final readings are both given.
- Express a calculated mean rate with the correct compound unit and an appropriate number of significant figures.
- Plot quantity against time accurately with labelled axes and suitable scales.
- Describe how the gradient of the curve relates to the rate of reaction.
- Explain what a plateau on the curve shows about the reaction.
- Draw an accurate tangent to a curve at a specified time.
- Use the slope of a tangent as a measure of the rate of reaction.
- Compare rates of reaction at different times by comparing the steepness of tangents.
- Draw a tangent to a rate curve at a specified time, including at t=0.
- Calculate the gradient of that tangent using two points on the line.
- Interpret the gradient as the rate of reaction at that specific time, including its units.
Calculating rates of reactions exam tips
Marking Points
- Rate can be followed by measuring a reactant being used up, such as the loss in mass of a reaction mixture when a gas escapes.
- Rate can be followed by measuring a product formed, such as the volume of gas collected in a gas syringe or the mass of precipitate formed.
- The quantity measured must be recorded at regular time intervals so that a rate can be calculated.
- The average rate over a time interval is the change in quantity divided by the time taken for that change.
- A graph of quantity against time allows the rate at any specific time to be found from the gradient of the tangent (Higher Tier only).
- The units of rate depend on the quantity measured and the time unit, for example cm³/s for gas volume or g/s for mass loss.
- Mean rate is calculated using: mean rate = quantity of reactant used ÷ time taken, or quantity of product formed ÷ time taken.
- The quantity of reactant used is always found by subtracting the final reading from the initial reading, regardless of the start time.
- The time taken is the duration of the interval in seconds, minutes or another consistent unit.
- The units of mean rate are the units of quantity divided by the units of time, such as cm³/s, g/s or mol/s (Higher Tier only).
- Rate at a particular moment can be found by drawing a tangent to the curve and calculating its gradient.
- State the relationship as mean rate of reaction = quantity of product formed ÷ time taken.
- Identify the quantity of product formed as the change in mass in g or volume in cm³ between two chosen times.
- Identify the time taken as the time interval in seconds over which that product quantity formed.
- Substitute measured values correctly and calculate the quotient without arithmetic error.
- Attach the correct compound unit, such as g/s or cm³/s, to the answer.
- Recognise that the value is a mean over the interval and that rate can change during a reaction.
- Identify mass in grams as a measurement of the quantity of reactant or product, often using a balance.
- Identify volume in cm³ as a measurement of the quantity of reactant or product, often using a gas syringe or measuring cylinder.
- Link mass loss to a gas escaping from an open reaction vessel.
- Link volume increase to a gas being produced and collected.
- Select a suitable measurement method for a described reaction and justify the choice.
- Record measurements at regular time intervals so that a rate can be calculated.
- State that rate of reaction is the change in amount of reactant or product divided by the time taken.
- Identify that a mass change measured in grams over time in seconds gives the unit g/s.
- Identify that a gas volume change measured in cm³ over time in seconds gives the unit cm³/s.
- Calculate a mean rate by dividing the measured change by the time taken and attach the correct unit.
- Recognise that the unit must match the quantity measured, so mass data give g/s and gas volume data give cm³/s.
- Calculate the amount of reactant in moles from mass and molar mass.
- Use rate = change in amount in moles ÷ time taken to find a rate in mol/s.
- Attach the unit mol/s correctly to a rate calculated from mole data.
- Convert between mass and moles before dividing by time when the question supplies mass data but requires mol/s.
- Interpret a rate in mol/s as the number of moles of reactant used or product formed each second.
- Use the equation mean rate = change in quantity ÷ time taken, stating it or applying it correctly.
- Calculate the change in quantity by subtracting the initial value from the final value when the measurement does not start at zero.
- Use the total time taken for that change, converting minutes to seconds or seconds to minutes when the required unit demands it.
- Divide the change in quantity by the time taken and round appropriately, for example 8.0 g ÷ 20 s = 0.40 g/s.
- Attach the correct compound unit to the answer, such as g/s, cm³/s or mol/s, derived from the quantity and time units.
- For a graph, read two points on the line, calculate the change in y and the change in x, then divide to find the mean rate over that interval.
- Axes are labelled with quantity (for example volume of gas in cm³ or mass in g) and time in s, with units stated.
- A sensible scale is chosen so the plotted points fill most of the grid, and points are plotted accurately.
- Points are joined with a smooth curve of best fit, not a series of straight lines or a dot-to-dot pattern.
- The gradient of the curve is described as the rate: a steeper curve means a faster reaction at that time.
- The plateau shows the reaction has finished because a limiting reactant has been used up, so the quantity no longer changes.
- A 'reactant used up' graph rises and flattens at a high value, whereas a 'reactant remaining' graph falls and flattens at a low value.
- A tangent is drawn as a straight line touching the curve at the required time and matching the curve's direction at that point.
- The slope of the tangent is used as a measure of the rate of reaction at that specific time.
- A steeper tangent is interpreted as a faster rate at that time, and a near-zero slope near the plateau as a very slow or stopped reaction.
- The tangent must only touch the curve at one point, rather than crossing it as a secant line.
- A tangent is a straight line drawn so it touches the curve at the required time and has the same slope as the curve at that point.
- The gradient is found by choosing two well-separated points on the tangent and dividing the change in the y-axis quantity by the change in time.
- The units of the gradient are the y-axis units divided by seconds, for example cm³ s⁻¹ for gas volume against time.
- A steeper tangent indicates a faster rate at that time; a shallower tangent indicates a slower rate.
- The tangent must be drawn at the specified time, which can include the start of the reaction (t=0) to calculate the initial rate, but avoid using arbitrary start or end points.
Examiner Tips
- 💡When describing a method, state the quantity you will measure, the time intervals, and how you will calculate the rate from the results.
- 💡If asked to compare rates, quote values with units and refer to the steepness of the graph.
- 💡For a tangent (Higher Tier only), draw it at the required time, make it as long as possible, and read the coordinates from points on the tangent to calculate the gradient.
- 💡Write down the equation, substitute the numbers with units, and give the answer with the correct unit.
- 💡If a graph is provided, read the quantity values from the graph at the start and end of the interval before calculating the mean rate.
- 💡Write the equation, then substitute values with units before calculating, so the examiner can follow your method.
- 💡If a graph is given, read two points on the line, find the change in the y-value and divide by the change in the x-value.
- 💡Check whether the question asks for the mean rate over a stated interval or the rate at a particular time, and answer the one requested.
- 💡Name the apparatus you would use, such as a balance for mass or a gas syringe for volume, to show your method is practical.
- 💡State the unit with every measurement, using g for mass and cm³ for volume.
- 💡When comparing methods, mention what is controlled, such as temperature or concentration, so the comparison is fair.
- 💡Always write the division explicitly, for example 24 cm³ ÷ 8 s = 3 cm³/s, so the unit is clearly earned.
- 💡Check whether the question gives mass or gas volume before choosing g/s or cm³/s.
- 💡If a graph is provided, read the change from the axis label and divide by the time interval to keep the unit consistent.
- 💡Show the mole calculation and the division by time as separate steps so both the amount and the rate unit are clear.
- 💡When a question gives mass and asks for mol/s, calculate moles first and then divide by the time taken.
- 💡Underline the quantity and the time in the question before calculating, so you use the right values.
- 💡Show the subtraction and division steps clearly; method marks may be available even if the final number is wrong.
- 💡Check that your unit matches the units in the data, and convert if the question asks for a different time unit.
- 💡Check the axis labels carefully: a rising curve means product formed or reactant used up, while a falling curve means reactant remaining.
- 💡Quote values from the graph with units when asked to interpret, such as the time taken to reach a certain volume.
- 💡If asked to compare two curves, refer to which is steeper and what that shows about rate, not just which is higher.
- 💡Use a ruler and a sharp pencil, and carefully align the ruler to match the curve's direction at the specific time.
- 💡Remember that comparing the steepness of tangents allows you to compare rates at different times without calculating the exact gradient.
- 💡Draw the tangent with a sharp pencil and a ruler, extending it clearly on both sides of the chosen point so two readable coordinates are available.
- 💡Choose coordinates that lie on the tangent and are far apart, as this reduces the effect of reading error on the gradient.
Common Mistakes
- Plotting time on the y-axis and quantity on the x-axis: this makes the gradient the reciprocal of the rate. Always put quantity on the y-axis and time on the x-axis.
- Confusing the total quantity measured with the rate: the total volume of gas collected is not the rate. Rate is the quantity changed per unit time, so divide by the time taken.
- Assuming the rate stays constant throughout: many reactions slow down as reactants are used up, so the gradient of a quantity-time graph decreases over time.
- Assuming the total amount of reactant at the end equals the amount used if the interval starts at zero: always calculate the difference between initial and final readings.
- Forgetting to include units or writing the units incorrectly, for example writing g instead of g/s: divide the quantity unit by the time unit.
- Dividing time by quantity instead of quantity by time: the equation is quantity ÷ time, so a larger quantity in the same time gives a larger rate.
- Dividing time by quantity instead of quantity by time; correct this by writing the equation first and checking that the larger quantity of product gives a larger rate.
- Using the total time from the start of the reaction when the interval begins later; correct this by subtracting the earlier time from the later time to find the interval.
- Omitting or miswriting the unit; correct this by dividing the unit of quantity by the unit of time, for example cm³ ÷ s = cm³/s.
- Using mass loss when the reaction is in a sealed vessel, so no gas escapes; correct this by choosing volume of gas produced instead.
- Confusing cm³ with cm² or writing the unit without the raised exponent; correct this by writing cm³ for volume.
- Recording only a single reading rather than a series over time; correct this by taking readings at regular intervals so a rate can be found.
- Writing the unit as g or cm³ without the per second part; correct this by remembering that rate always involves time, so the unit must include /s.
- Dividing time by the change instead of change by time; correct this by using rate = change ÷ time.
- Using g/s for a gas volume measurement or cm³/s for a mass measurement; correct this by matching the unit to the quantity actually measured.
- Dividing mass by time and labelling the answer mol/s; correct this by first converting mass to moles using moles = mass ÷ molar mass.
- Forgetting to include the time unit and writing only mol; correct this by remembering that rate is per second, so the unit is mol/s.
- Using the relative formula mass as the number of moles; correct this by dividing the given mass by the relative formula mass to find moles.
- Using the final reading as the change in quantity without subtracting the initial reading; correct this by calculating final minus initial.
- Mixing units, for example dividing grams by minutes but writing g/s; correct this by converting time to seconds or writing g/min.
- Confusing mean rate with instantaneous rate and reading a single point from a graph; correct this by using two points and the change in y divided by the change in x.
- Joining the points with straight lines instead of a smooth curve: correct this by drawing one continuous curve that passes as close as possible to all the points.
- Forgetting units on the axes: correct this by writing, for example, 'volume of gas / cm³' and 'time / s' on the labels.
- Reading the plateau as the reaction speeding up: correct this by explaining that a flat line means no further change, so the rate is zero because a reactant is exhausted.
- Drawing the tangent through two points on the curve instead of touching it at one point: correct this by placing the line so it just touches the curve at the chosen time and follows its slope.
- Assuming drawing tangents is only for Higher Tier students: all students must be able to draw tangents and use the slope to compare rates.
- Using the whole curve's average slope when asked for the rate at a specific time: correct this by drawing the tangent at that time only.
- Drawing the tangent so it crosses the curve instead of touching it at one point: redraw the line so it just touches the curve at the required time and follows the curve's direction there.
- Using the whole graph's start and end points rather than the tangent: the gradient of a chord gives an average rate, not the rate at a specific time.
- Forgetting to include units or inverting the division: divide the change in the y quantity by the change in time and give units such as cm³ s⁻¹.