13.5 - Reading & Interpreting Graphs
Graph-reading questions
Graph-reading questions usually ask you to:
- Read a particular value off the line
- Read the value where two lines meet
- Describe the trend shown by the line
A typical example
Aqueous sodium carbonate is added to a fixed volume of aqueous barium nitrate, forming a white precipitate of barium carbonate.
The graph shows how the height of the precipitate formed changes with the volume of aqueous sodium carbonate added.
(a) Use the graph to find the height of precipitate formed when 3.5 cm3 of aqueous sodium carbonate is added. [2]
(b) Describe how the height of precipitate changes as the volume of aqueous sodium carbonate increases. [2]
Where the marks are
- (a) The value read off the line, and the dashed construction lines drawn on the graph to show where it came from.
- (b) The direction (height increases as more is added), backed by figures, plus the point where the line levels off.
Reading a value off a graph
- To read a value off a graph:
- Go up from the value on the x-axis to the line of best fit.
- Go across to the y-axis and read the value.
- Always draw both dashed construction lines on the graph - mark schemes award marks for showing your working.
Interpolation vs extrapolation
- Interpolation - Reading a value between plotted points. This is the standard method.
- Extrapolation - Reading a value beyond your plotted points by extending the line of best fit.
- Only extrapolate when a question specifically asks you to (e.g. extending a solubility curve beyond your highest measured temperature). Otherwise, stay within your plotted data.
Reading the point where two lines meet
Some experiments produce data with two distinct linear trends rather than a single curve. The required value is the point where the two straight lines intersect.
Rising then level
- In a precipitation reaction, precipitate height increases as reagent is added, then stays constant once the other reactant is fully used up.
- Draw two straight lines with a ruler: one through the rising points and one through the flat points.
- Extend both lines until they cross:
- Volume at crossing point = volume needed to react completely with the reactant.
- Height at crossing point = maximum height of precipitate produced.
Rising then falling
- In a neutralisation reaction between dilute acid and alkali where total volume is kept constant, temperature rises to a peak at neutralisation, then falls as excess solution cools the mixture.
- Draw a straight line through the rising points and a second straight line through the falling points, then extend them until they cross.
- The volume at the intersection shows the exact volume needed for neutralisation - a value that may not appear in the raw data table.
How to find the intersection
- Draw two separate straight lines through each set of points using a ruler (do not draw a curve).
- Extend both lines until they cross.
- Read the value at the crossing point using dashed construction lines.
Describing a trend
A complete description of a trend requires three parts:
- The direction of the relationship (e.g. increases or decreases).
- Data from the axes to support the statement.
- Any change in behaviour, such as where the line levels off or peaks.
Sentence frame
As [independent variable] increases, [dependent variable] increases / decreases from [initial value] to [value], then levels off at [value].
- Example - "As the volume of sodium carbonate increases, the height of the precipitate increases from 0 to 70 mm, then levels off once 6 cm3 has been added."
- Either direction is accepted if scientifically correct (e.g. "solubility increases as temperature increases" or "solubility decreases as temperature decreases").
Common exam questions
Question 1
What is the difference between interpolation and extrapolation?
Interpolation is reading a value between your plotted points, which is the normal case; extrapolation is reading a value beyond your last point, which is riskier because there are no readings out there to check the line against.
Question 2
Why does a correct reading sometimes not score full marks?
Because a mark is given for the construction lines that show where the reading came from, separately from the value itself; a number with no lines to support it can lose that mark.
Question 3
In a precipitate experiment, the height of solid rises then stays constant as more reagent is added. How do you find the volume at which the reaction is exactly complete?
Draw a straight line through the rising points and a straight line through the flat points, extend both with a ruler until they cross, and read the volume at the point where they meet.
Question 4
In a neutralisation experiment where different volumes of dilute hydrochloric acid and aqueous sodium hydroxide are mixed, keeping the total volume constant, the highest temperature recorded rises then falls as more sodium hydroxide is used. Why is the peak temperature not simply the highest reading in the table?
Because the true peak usually falls between two of the volumes actually tested, not on one of them; two straight lines are drawn through the rising and falling points and extended until they cross, and the peak is read at that crossing point.
Question 5
What three things does a good description of a trend need?
The direction the line goes, some figures from the axes to back it up, and any change in behaviour, such as where the line levels off.
Question 6
A student describes a trend by writing "the height goes up". Why does this not get full marks?
It gives a direction but no figures from the axes and no mention of where the line levels off, so it is missing two of the three things a trend answer needs.
Question 7
A mark scheme accepts both "solubility increases as temperature increases" and "solubility decreases as temperature decreases" for the same graph. Why are both correct?
Because they describe the same relationship read in opposite directions; either wording links the two variables and gives the correct direction between them.