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IBChemistryDPHLFlashcardsToolsTool 3: Mathematics

Tool 3: Mathematics (DP IB Chemistry)

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  • What is the mean average?

    The mean average is the total of all the values divided by the number of values.

  • State two places where the mean average is used in chemistry.

    Two places where the mean average is used in chemistry are:

    • Titrations, calculating the average titre

    • Relative atomic mass, calculating Ar from isotopic abundance data

  • What is the mean average of 30, 32 and 32?

    The mean average of 30, 32 and 32 is:

    • (30 + 32 + 32) / 3 = 31.3

  • What is the mean average of 20.1, 20.2, 20.3 and 22.2?

    The mean average of 20.1, 20.2, 20.3 and 22.2 is:

    • (20.1 + 20.2 + 20.3) / 3 = 20.2

    22.2 should not be included in the calculation as it is an anomalous result.

  • Define the term range.

    Range is a measure of how spread out data is, calculated as the difference between the highest and lowest values.

  • What is an order of magnitude?

    An order of magnitude is when a number is expressed to an order of 10, e.g. 2.5 x 10-3.

  • Define approximation.

    Approximation is finding a value that is close to the actual value of a quantity.

  • True or False?

    Percentage change and percentage difference are the same.

    False.

    Percentage change expresses the relative change between an initial and final value.

    Percentage difference compares two values to determine how much they differ as a percentage.

  • State the equation for percentage change.

    The equation for percentage change is:

    Percentage change = ( (Final Value - Initial Value) / Initial value) × 100

  • During the course of a chemical reaction, the initial concentration of A increases from 0.25 mol dm–3 to 0.28 mol dm–3.

    Calculate the percentage change in concentration.

    The percentage change is:

    • Percentage change = fraction numerator left parenthesis Final space Value minus Initial space Value right parenthesis over denominator Initial space value end fraction cross times 100

    • Percentage change = fraction numerator open parentheses 0.28 minus 0.25 close parentheses over denominator 0.25 end fraction cross times 100 = 12%

    • So, the concentration of the A increased by 12% during the reaction

  • What is percentage error?

    Percentage error is used to express the difference between a final calculated answer and an accepted or literature value.

  • By experiment, the enthalpy of combustion of propan-1-ol was found to be –1.85 x 103 kJ mol–1.

    The literature value for this enthalpy change is -2021 kJ mol-1.

    Calculate the percentage error.

    The percentage error is:

    • Percentage error = fraction numerator accepted space value minus experimental space value over denominator accepted space value end fraction cross times 100

    • Percentage error = fraction numerator open parentheses negative 2021 close parentheses minus open parentheses negative 1850 close parentheses over denominator open parentheses negative 2021 close parentheses end fraction cross times 100 = 8.5%

  • List four types of percentage that can be calculated in chemistry.

    Types of percentage that can be calculated in chemistry include:

    • Percentage yield

    • Percentage atom economy

    • Percentage change

    • Percentage difference

    • Percentage error

    • Percentage uncertainty

  • State two places where reciprocals are used in calculations.

    Two places where reciprocals are used in calculations are:

    • Gas laws, using 1 / V,

    • Concentration versus rate graphs, using 1 / T.

  • True or False?

    pH and Arrhenius calculations involve logarithmic and exponential calculations.

    False.

    pH calculations involve logarithmic calculations.

    Arrhenius calculations involve logarithmic and exponential calculations.

  • What are the common units for concentration?

    The common units for concentration are:

    • mol dm-3

  • What are the common units for enthalpy?

    The common units for enthalpy are:

    • kJ mol-1

  • What are the common units for entropy?

    The common units for entropy are:

    • J K-1 mol-1

  • Write 0.62748 to 3 significant figures.

    0.62748 to 3 significant figures is 0.627.

  • Write 0.57391 in standard form, to 3 significant figures.

    0.57391 in standard form, to 3 significant figures, is 5.74 x 10-1.

  • True or False?

    At the end of a calculation, the number of significant figures should not exceed the value with the least number of significant figures used in the calculation.

    True.

    At the end of a calculation, the number of significant figures should not exceed the value with the least number of significant figures used in the calculation.

  • Calculate the number of moles in 25.5 cm3 of a 0.25 mol dm–3 solution of HCl.

    Give your answer to an appropriate number of significant figures.

    The number of moles in 25.5 cm3 of a 0.25 mol dm–3 solution of HCl is:

    • Convert 25.5 cm3 to dm3 

      • fraction numerator 25.5 over denominator 1000 end fraction = 0.0255 dm3

    • Moles = concentration x volume

      • Moles = 0.25 x 0.0225 = 6.375 x 10–3 

    • Volume is given to 3 significant figures and concentration is given to 2 significant figures

    • So, the final answer is 6.34 x 10–3 moles

  • What is uncertainty in chemistry?

    Uncertainty is a quantitative indication of the quality of a result, representing the difference between the actual reading taken and the true value.

  • Define absolute uncertainty.

    Absolute uncertainty is the actual amount by which a quantity is uncertain.

  • What is fractional uncertainty?

    Fractional uncertainty is the absolute uncertainty divided by the quantity itself.

  • State the equation for percentage uncertainty.

    The equation for percentage uncertainty is:

    Percentage uncertainty = (uncertainty / measured value) × 100

  • True or False?

    Uncertainties are the same as errors in measurements.

    False.

    Uncertainties are not the same as errors.

    Errors arise from equipment or practical techniques that cause a reading to be different from the true value.

  • How do you propagate uncertainties when adding or subtracting measurements?

    When adding or subtracting measurements, you add the absolute measurement uncertainties.

  • How do you propagate uncertainties when multiplying or dividing measurements?

    When multiplying or dividing experimental measurements, you add together the percentage uncertainties.

  • What is the coefficient of determination?

    The coefficient of determination, R2, is a measure of fit that can be applied to lines and curves on graphs.

  • True or False?

    An R2 value of 0 means the dependent variable can be perfectly predicted from the independent variable.

    False.

    An R2 value of 0 means the dependent variable cannot be predicted from the independent variable.

  • What does an R2 value of 1 indicate?

    An R2 value of 1 indicates that the dependent variable can be perfectly predicted from the independent variable, and the trend line/curve is a perfect fit.

  • What is the volume, including uncertainty, for this final reading from a burette?

    A reading from a burette

    The volume, including uncertainty, for the final reading from a burette is:

    • 13.2 cm3 plus-or-minus 0.05 cm3

Previous:Tool 1: Experimental Techniques

    1. Topic 1

      Introduction to the Particulate Nature of Matter

    2. Topic 2

      The Nuclear Atom

    3. Topic 3

      Electronic Configurations

    4. Topic 4

      Counting Particles by Mass: The Mole

    5. Topic 5

      Ideal Gases

    1. Topic 1

      The Ionic Model

    2. Topic 2

      The Covalent Model

    3. Topic 3

      The Metallic Model

    4. Topic 4

      From Models to Materials

    1. Topic 1

      The Periodic Table: Classification of Elements

    2. Topic 2

      Functional Groups: Classification of Organic Compounds

    1. Topic 1

      Measuring Enthalpy Change

    2. Topic 2

      Energy Cycles in Reactions

    3. Topic 3

      Energy from Fuels

    4. Topic 4

      Entropy & Spontaneity

    1. Topic 1

      How Much? The Amount of Chemical Change

    2. Topic 2

      How Fast? The Rate of Chemical Change

    3. Topic 3

      How Far? The Extent of Chemical Change

    1. Topic 1

      Proton Transfer Reactions

    2. Topic 2

      Electron Transfer Reactions

    3. Topic 3

      Electron Sharing Reactions

    4. Topic 4

      Electron Pair Sharing Reactions

    1. Topic 1

      Tool 1: Experimental Techniques

    2. Topic 2

      Tool 3: Mathematics