# Predictions from Graphs

## Key Concepts

• Graphs are useful in Chemistry because they allow us to make predictions.

(a) between two known points on the graph (interpolation)

(b) before the first known point on the graph (extrapolation)

(c) after the last known point on the graph (extrapolation)

• Interpolate means to insert points between known points on the graph.

• Extrapolate means to insert points either before the first known point, or, after the last known point on the graph.

• Interpolated lines on a graph are drawn as solid lines between plotted points.

• Extrapolated lines on a graph are draw as dotted lines (or sometimes dashed lines) beyond the known plotted points.

• There are limits to how far a line on a graph should be extrapolated.

## Why Draw a Graph?

There are two really good reasons for drawing a graph to represent numerical data:

• A graph conveys a lot of information very quickly.

• A graph can be used to make predictions.

Sometimes these predictions can be the difference between life and death!

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## Interpolation

Predicting the value of a point on the graph that occurs between two known points on the same graph is known as interpolation.

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Interpolation assumes that the overall relationship described for the known points is also true between known points.
This is almost always a good assumption, so there is very little risk in making predictions from a graph using interpolation.

## Extrapolation

Extrapolation means extending the line of best fit past the last known point.

It is important that we distinguish the "known" parts of the graph from the "extrapolated" parts of the graph because we really can't be sure if our assumption is good or not.
When you draw a graph, you will use a solid line for the parts of the graph that are "known", and dashed or dotted lines for those parts of the graph which are extrapolated past the known points.

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Predicting the value of a point on the graph that occurs either before the first known point on the graph or after the last known point on the graph is known as extrapolation.

Extrapolation assumes that the overall relationship described for the known points is also true for points before the first known value and points after the last known value.
Often this assumption is not good in chemistry. There is a lot of risk in making predictions from a graph using extrapolation. There are limits to how far many graphs can be extrapolated in chemistry.
For this reason, you should never extrapolate a line too far from the known points.

## Extrapolation Limits

Extrapolation assumes that the relationship between known or measured x values and y values will also be true for unknown or unmeasured x values and y values.
This is not always a good assumption.
We have to use our "chemical sense" to decide if we can extrapolate the line on a graph or not.

Often we want to extrapolate a known line back until it meets either the x axis (0,y), or the y axis (x,0), or the origin (0,0).
When we do this, we should ask ouselves if this makes sense from a "chemistry point of view".

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*This discussion assumes that all species are present in their standard states so that the electrode potentials are standard electrode potentials.

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