Interactions of Limiting Factors

Worked Example

A student is investigating photosynthesis and moves a lamp from a distance of $10\text{ cm}$ away from a pondweed plant to $30\text{ cm}$ away. Calculate the new relative light intensity compared to the original position.

Step 1: Calculate the distance factor.

• $30\text{ cm} / 10\text{ cm} = 3$. The distance has tripled ($3\times$).

Step 2: Apply the inverse square law by squaring the distance factor.

• $3^2 = 9$

Step 3: State the change.

• The new light intensity is $1/9$ of the original value.

Carbon Dioxide Concentration

• Carbon dioxide is a raw material required for the reaction. In the natural atmosphere, it makes up only about $0.04\%$, which is often the limiting factor on a sunny day.
• Increasing the concentration of $\text{CO}_2$ increases the frequency of successful collisions between the reactant molecules and the enzymes inside the chloroplasts.
• Commercial greenhouses often pump in extra $\text{CO}_2$ (up to $0.1\%$) to drive the reaction forward faster, significantly increasing crop yields.

Temperature and Enzyme Action

• Photosynthesis is driven by a series of enzyme-controlled reactions. Temperature affects how fast these enzymes can work.
• As the temperature increases towards the optimum temperature (usually between $25^\circ\text{C}$ and $35^\circ\text{C}$), the particles gain kinetic energy. Both the enzymes and the substrate molecules move faster, leading to more frequent successful collisions and the formation of more enzyme-substrate complexes.
• If the temperature rises too high (typically above $40^\circ\text{C}$ to $45^\circ\text{C}$), the extreme thermal energy breaks the chemical bonds holding the enzyme's 3D structure together.
• The active site undergoes denaturation and permanently changes shape. It is no longer complementary to the substrate, and the rate of photosynthesis plummets to zero.

Interpreting Interaction Graphs

• Examiners frequently ask you to interpret graphs showing the rate of photosynthesis against a limiting factor. The shape of the curve reveals how different factors interact.
• The Upward Slope: While the line is sloping upwards, the factor on the x-axis (e.g., light intensity) is actively limiting the rate. Increasing it causes a proportional increase in photosynthesis.
• The Plateau: Eventually, the graph levels off and becomes horizontal. At this point, increasing the x-axis factor has no further effect. This happens because another factor (like temperature or $\text{CO}_2$) is now in shorter supply and has taken over as the limiting factor.
• Farmers manipulate these interactions using paraffin heaters, which provide a double benefit: they increase the temperature while releasing $\text{CO}_2$ as a byproduct of combustion, ensuring neither factor limits the plant's growth.

Chlorophyll and Plant Health

• Sometimes, the physical condition of the plant limits photosynthesis. The rate depends directly on how much chlorophyll is present to absorb light.
• Diseases like Tobacco Mosaic Virus (TMV) or a lack of magnesium in the soil can cause chlorosis (the yellowing of leaves). Without enough chlorophyll, less light energy is absorbed, severely restricting the rate of photosynthesis regardless of environmental conditions.