Mean decay rate uses change per time
Definition
Rate of decay
The amount of biological material decomposed per unit time.
- The amount decomposed can be measured as a decrease in mass, volume or another stated quantity.
- For mass data, calculate Δm=minitial−mfinal\Delta m=m_{\text{initial}}-m_{\text{final}}Δm=minitial−mfinal before calculating the rate.
- The mean rate is mean rate of decay=amount decomposedtime taken\text{mean rate of decay}=\frac{\text{amount decomposed}}{\text{time taken}}mean rate of decay=time takenamount decomposed.
- For mass loss, mean rate=minitial−mfinalΔt\text{mean rate}=\frac{m_{\text{initial}}-m_{\text{final}}}{\Delta t}mean rate=Δtminitial−mfinal.
- A suitable unit is g d−1\mathrm{g\,d^{-1}}gd−1 when mass is measured in grams and time in days.
Example
- A leaf sample decreases from 180 g180\,\mathrm{g}180g to 132 g132\,\mathrm{g}132g in 30 d30\,\mathrm{d}30d.
- The mass decomposed is 180−132=48 g180-132=48\,\mathrm{g}180−132=48g.
- The mean rate is 48 g30 d=1.6 g d−1\frac{48\,\mathrm{g}}{30\,\mathrm{d}}=1.6\,\mathrm{g\,d^{-1}}30d48g=1.6gd−1.
- A second sample decaying at 1.2 g d−11.2\,\mathrm{g\,d^{-1}}1.2gd−1 is slower by 0.4 g d−10.4\,\mathrm{g\,d^{-1}}0.4gd−1.
Use the elapsed time, not the reading count
- The time interval is Δt=tfinal−tinitial\Delta t=t_{\text{final}}-t_{\text{initial}}Δt=tfinal−tinitial, even when the table contains several intermediate readings.
- Intermediate values are not added when the question asks for the mean rate between two named times.
- Keep unrounded values during working and round only the final answer to a sensible number of significant figures.
- Include the unit because a numerical rate without amount per time is incomplete.
Exam technique
- Subtract the two endpoint quantities, then divide by the elapsed time, not by the number of rows in the table.
- Show the subtraction and division because each stage can earn credit even if the final number is wrong.
- Check whether the question asks for mass lost, mass remaining or percentage change before choosing the numerator.
Percentage changes compare samples fairly
- The percentage mass lost is percentage mass lost=minitial−mfinalminitial×100\text{percentage mass lost}=\frac{m_{\text{initial}}-m_{\text{final}}}{m_{\text{initial}}}\times100percentage mass lost=minitialminitial−mfinal×100.
- The percentage change in rate is percentage change=new rate−original rateoriginal rate×100\text{percentage change}=\frac{\text{new rate}-\text{original rate}}{\text{original rate}}\times100percentage change=original ratenew rate−original rate×100.
- A negative percentage change shows that the rate decreased, while a positive value shows that it increased.
- Percentages allow samples with different starting masses or original rates to be compared on the same scale.
Graphs show changes through time
- On a mass-remaining graph, a steeper downward section represents a faster rate of decomposition.
- The mean rate between two times is the magnitude of the gradient of the line joining those points.
- For a curve, a tangent at one time estimates the instantaneous rate using rate=∣ΔyΔx∣\text{rate}=\left|\frac{\Delta y}{\Delta x}\right|rate=ΔxΔy.
- Read both axes and their units before substituting values because time may be given in hours, days or weeks.
Example
- If the mass falls by 24 g24\,\mathrm{g}24g over 12 d12\,\mathrm{d}12d, the gradient is −2412=−2 g d−1\frac{-24}{12}=-2\,\mathrm{g\,d^{-1}}12−24=−2gd−1.
- The negative gradient shows that mass remaining decreases, while the rate of decay is usually reported as the positive magnitude 2 g d−12\,\mathrm{g\,d^{-1}}2gd−1.
Rate comparisons need the same basis
- Compare rates only after converting them to the same units and checking that they describe the same measured quantity.
- A fair conclusion states which sample decayed faster and supports it with the calculated rates.
- Differences in temperature, water or oxygen can explain a difference in rate by changing decomposer activity.
Self review
- Write the equation for mean rate of decay.
- Why is the number of table readings not used as the time denominator?
- What does a steeper downward mass graph show?
- How do you calculate percentage mass lost?
