Imagine looking at a car's speedometer during a journey: your speed at one exact second is very different from your average speed for the whole trip. In chemistry, we use graphs to find the rate of reaction at specific moments by looking at the steepness of the curve. The rate of reaction at any exact point on a curve is equal to the gradient (slope) of the graph at that point. The steeper the gradient, the faster the reaction is happening. If the line becomes perfectly horizontal, the gradient is zero, which tells us the reaction has finished.
Chemists measure reaction rates in two different ways depending on what information is needed. The instantaneous rate is the speed of the reaction at one specific "instant" in time, which requires drawing a straight line against the curve. In contrast, the mean rate is the average speed over a whole time interval, such as between 10 seconds and 40 seconds. Calculating the mean rate does not require drawing any extra lines; you simply divide the total change in the measured quantity by the total time taken.
To find the instantaneous rate, you must draw a tangent. A tangent is a straight line that touches a curve at a single point without crossing through it at that point.
Once your tangent is drawn, you can find the gradient by constructing a large right-angled triangle using the tangent as the hypotenuse. The larger your triangle, the more accurate your final reading will be.
The gradient is calculated using this formula:
A student investigates the reaction between magnesium and hydrochloric acid by measuring the volume of hydrogen gas produced over time. Calculate the rate of reaction at exactly 25 seconds.
Step 1: Locate 25 seconds on the x-axis, find the corresponding point on the curve, and draw a tangent.
Step 2: Construct a large right-angled triangle on the tangent and pick two easy-to-read coordinates.
Step 3: Calculate the change in y () and the change in x ().
Step 4: Substitute the values into the gradient formula.
Step 5: Calculate the final answer and include appropriate units.
Sometimes, an exam question will ask for the initial rate of a reaction. This is simply the instantaneous rate at the very start of the reaction (). To find this, draw your tangent touching the curve exactly at the origin and calculate its gradient.
When calculating the rate at a specific time, you must avoid interpolation. Interpolation means taking a direct reading from a point on the curve (just reading the y-value and dividing it by the x-value). This is mathematically incorrect for finding the instantaneous rate on a curve because it does not use the slope. You must physically draw the tangent to calculate the true gradient.
Students often try to find the rate at a specific time by simply dividing the y-axis value by the x-axis value (interpolation); you MUST draw a tangent to get the correct instantaneous rate.
Always draw your tangent as long as possible so that it crosses the x-axis and y-axis; constructing a larger triangle reduces your percentage error when reading values.
OCR examiners look for the physical line of your tangent on the graph — if you calculate the correct rate but haven't drawn the tangent, you will lose method marks.
Always check the scale of the y-axis carefully before calculating your change in y, especially on mass-loss graphs which often start at 100g rather than 0g.
Give your final answer to the same number of significant figures as the data provided in the question (usually 2 or 3 significant figures).
Rate of reaction
The change in the amount or concentration of a reactant or product per unit of time.
Gradient
The steepness of a line, calculated as the vertical change divided by the horizontal change, representing the rate of reaction on a rate graph.
Instantaneous rate
The rate of a reaction at one specific moment in time, calculated by finding the gradient of a tangent drawn at that exact point on a curve.
Mean rate
The average rate of a reaction over a specific time interval, calculated by dividing the total change in a quantity by the total time taken.
Tangent
A straight line that touches a curve at a single point without crossing through it, representing the slope of the curve at that exact moment.
Initial rate
The rate of a reaction at the very start (at 0 seconds), determined by drawing a tangent at the origin of a rate graph.
Interpolation
Taking a direct reading from a point on the curve, which is an incorrect method for finding the instantaneous rate of a curve.
Put your knowledge into practice — try past paper questions for Chemistry A
Rate of reaction
The change in the amount or concentration of a reactant or product per unit of time.
Gradient
The steepness of a line, calculated as the vertical change divided by the horizontal change, representing the rate of reaction on a rate graph.
Instantaneous rate
The rate of a reaction at one specific moment in time, calculated by finding the gradient of a tangent drawn at that exact point on a curve.
Mean rate
The average rate of a reaction over a specific time interval, calculated by dividing the total change in a quantity by the total time taken.
Tangent
A straight line that touches a curve at a single point without crossing through it, representing the slope of the curve at that exact moment.
Initial rate
The rate of a reaction at the very start (at 0 seconds), determined by drawing a tangent at the origin of a rate graph.
Interpolation
Taking a direct reading from a point on the curve, which is an incorrect method for finding the instantaneous rate of a curve.