Units, rates and constants from data

Checking and correcting units

• A rate has units of quantity per time: cm³ min⁻¹, mm³ s⁻¹, µm h⁻¹.
• A gradient's unit is y unit ÷ x unit.
• Volumes of gas in a capillary: V = πr²l gives mm³ if r and l are in mm.
• Convert carefully: the October 2023 mark scheme accepted 6.1 to 6.5 cm³ s⁻¹ or 366 to 390 cm³ min⁻¹ or the equivalent in dm³, but not a wrong unit.
• Spotting errors in a student table: a column in g with one value clearly in mg, a heading with no unit, seconds and minutes mixed.

Temperature coefficient Q10 (CP12)

Q10 = rate at (T + 10) °C ÷ rate at T °C

If development is measured as time, first convert to rate (rate = 1 / time). Q10 of about 2 to 3 is typical of enzyme-controlled processes between about 10 and 30 °C. See Climate change, temperature and Q10 (Unit 4) for the method.

Constants from graphs

• Gradient of a straight line = the constant in y = mx + c (for example rate of oxygen uptake from a respirometer distance-time graph).
• Intercept: the compensation point (where net gas exchange is zero) or the concentration of no change in mass.
• From a log graph: the gradient of the straight log phase gives a growth rate constant.

Always quote the constant with its unit and a sensible number of significant figures.

Worked example

Fruit fly larvae take 20 days to develop at 15 °C and 8 days at 25 °C. Calculate Q10.

1. Rates: 1/20 = 0.05 day⁻¹ and 1/8 = 0.125 day⁻¹
2. Q10 = 0.125 / 0.05 = 2.5

Answer: Q10 = 2.5

Check yourself

1. Eggs hatch in 30 days at 10 °C and 12 days at 20 °C. Calculate Q10.
   Show answer

   2.5. Rates 1/30 and 1/12; Q10 = (1/12) / (1/30) = 30 / 12 = 2.5.

2. The rate of a process is 0.36 units min⁻¹ at 25 °C and 0.15 units min⁻¹ at 15 °C. Calculate Q10.
   Show answer

   2.4. 0.36 / 0.15 = 2.4.

3. A bubble moves 30 mm along a capillary of radius 0.5 mm. Calculate the volume of gas in mm³ to 3 significant figures.
   Show answer

   23.6 mm³. π x 0.25 x 30 = 23.6 mm³.

4. Convert 0.38 dm³ min⁻¹ to cm³ s⁻¹ to 2 significant figures.
   Show answer

   6.3 cm³ s⁻¹. 380 / 60 = 6.33 cm³ s⁻¹, so 6.3 to 2 s.f.

5. A table column headed 'Rate of oxygen uptake / mm³' is wrong. What should the unit be?
   • mm
   • mm³ min⁻¹ (or another volume per time unit)
   • min
   • No unit
   Show answer

   mm³ min⁻¹ (or another volume per time unit). A rate is per unit time.

6. A graph of distance moved by fluid (mm) against time (min) is a straight line. What does its gradient give?
   • Total oxygen used
   • The RQ
   • The temperature coefficient
   • Rate of movement in mm min⁻¹, proportional to the rate of oxygen uptake
   Show answer

   Rate of movement in mm min⁻¹, proportional to the rate of oxygen uptake. Gradient = y unit per x unit.

7. A calculated Q10 of 2.4 for development between 15 and 25 °C suggests what?
   • The process is purely physical
   • The process is controlled by enzymes
   • The organism is dead
   • Temperature has no effect
   Show answer

   The process is controlled by enzymes. Q10 of about 2 to 3 is typical of enzyme-controlled reactions.

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Sources

• Pearson Edexcel International Advanced Level in Biology specification (XBI11/YBI11, first teaching 2018): Unit 3, Unit 6 and Appendix 6 mathematical skills
• Pearson mark scheme WBI16/01, October 2023 (via Physics & Maths Tutor)

Last updated 8 November 2026. Spotted a mistake? Tell us.