IB DP Chemistry: SL复习笔记11.2.6 Analysing Graphs

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

1.8-Reaction-Kinetics-Rate-during-Reaction

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

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

Exam 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 cms-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:1.2.5-Graphs-of-Boyles-Law

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?11.2.6-Graphical-Relationships-Worked-Example

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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