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Last exams 2024

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Analysing Graphs (DP IB Chemistry: SL)

Revision Note

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Analysing Graphs

  • The gradient of a graph can be found by:
    • In the case of a straight line graph: using a triangle and the equation for a straight line
    • In the case of a curve: drawing a tangent to the graph

  • The triangle should be as large as possible to minimise precision errors
  • The equation for a straight line is y = mx + c, where:
    • y = dependent variable
    • x = independent variable
    • m = slope
    • c = y-intercept

  • The gradient or slope is therefore : m = ∆y/∆x
  • This example from Kinetics illustrates the calculation of rates from a curve

Reaction Kinetics Rate during Reaction, downloadable AS & A Level Chemistry revision notes

The gradient can be found at different points on a curve. Here it has been multiplied by 60 to convert it from minutes-1 to seconds-1

  • In the case of curves you will need a ruler to line up against the curve at the point you want to measure the gradient:

Tangent initial reaction rate (3), downloadable AS & A Level Biology revision notes

Lining up a ruler against the curve is essential to drawing a tangent accurately

Examiner Tip

Be careful that you process the units correctly when finding the gradient. The gradient unit is the y-unit divided by the x-unit, so in the example above the gradient of the curve is measured in cm3 s-1

Sketched Graphs

  • Sketched graphs are a way to represent qualitative trends where the variables shown are often proportional or inversely proportional
  • Sketched graphs do not have scales or data points, but they must have labels as these examples from the Gas Laws show:Graphs of Boyle’s Law, downloadable IB Chemistry revision notes

Sketched graphs show relationships between variables

Graphical Relationships

  • In the first sketch graph above you can see that the relationship is a straight line going through the origin
  • This means as you double one variable the other variable also doubles so we say the independent variable is directly proportional to the dependent variable
  • The second sketched graph shows a shallow curve which is the characteristic shape when two variables have an inversely proportional relationship
  • The third sketched graph shows a straight horizontal line, meaning as the independent variable (x-axis) increases the dependent variable does not change or is constant

Worked example

Which graph shows the correct relationship between the number of moles of a gas, n, and the temperature, T, at constant pressure and volume?

Answer:

The correct option is D

    • The Ideal Gas Equation is PV= nRT.
    • If P, V and R are constant then PV/R = nT = a constant
    • n must be inversely proportional to T, which gives graph D

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Stewart

Author: Stewart

Expertise: Chemistry Lead

Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Exam Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.