Limiting Factors

The Effect of Temperature

Imagine trying to type an essay outside in freezing weather versus sitting in a comfortable, warm room. Plants also have a specific preferred temperature for their internal chemistry to function efficiently.

• As temperature increases, the kinetic energy of both the substrate molecules and the enzymes increases.
• This extra kinetic energy makes the particles move much faster, leading to a higher frequency of successful collisions between the substrates and the enzyme active sites.
• The rate of photosynthesis reaches its peak at the optimum temperature, which is typically around 25°C for many temperate plants.
• If the temperature continues to rise beyond the optimum (usually above 40°C), the intense vibrations break internal hydrogen bonds within the enzyme.
• This causes denaturation, where the three-dimensional shape of the active site permanently changes.
• The active site is no longer complementary to the substrate, meaning the reaction stops entirely and the rate drops to zero.

The Effect of Light Intensity and the Inverse Square Law

Moving a reading lamp just a few centimetres further away from your desk makes a surprisingly big difference to how well you can see. The same mathematical rule applies to plants absorbing light energy.

• Light provides the essential energy required for the light-dependent stage of photosynthesis to proceed.
• When light is the limiting factor, the rate of photosynthesis is directly proportional to the light intensity.
• Eventually, the graph of rate against light intensity forms a plateau (levels off) because another factor, such as temperature or carbon dioxide, becomes the new limiting factor.
• Light intensity follows the inverse square law, meaning it is inversely proportional to the square of the distance from the source.
• When testing this in the lab (such as Edexcel's Core Practical), scientists often use algal beads placed in a bicarbonate indicator to measure the pH change as carbon dioxide is consumed.
• A glass tank of water is normally placed between the lamp and the plant to act as a heat filter, preventing temperature from becoming a confounding variable. Light intensity is often measured in arbitrary units (a.u.) when absolute measurements are not necessary.

Worked Example

A student investigates photosynthesis by placing a desk lamp 20 cm away from a beaker containing aquatic plants. Calculate the relative light intensity at this distance.

Step 1: Write out the formula.

• $\text{Light Intensity} \propto \frac{1}{d^2}$

Step 2: Substitute the distance ($d = 20$) into the equation.

• $\text{Light Intensity} \propto \frac{1}{20^2}$

Step 3: Calculate the final answer and include units.

• $\text{Light Intensity} = \frac{1}{400} = 0.0025$ a.u.

The Effect of Carbon Dioxide Concentration

Carbon dioxide makes up a tiny fraction of the air we breathe—only about 0.04%—which means plants are constantly scrambling to absorb enough of it to survive.

• Carbon dioxide is a crucial raw material used in the production of glucose.
• Increasing the concentration of $CO_2$ leads to more frequent successful collisions between the carbon dioxide molecules and the photosynthetic enzymes.
• Just like light intensity, the rate of reaction will initially rise linearly but will eventually hit a plateau when a different environmental factor holds the process back.
• Commercial farmers often exploit this by using paraffin heaters in their greenhouses, which simultaneously provide heat to approach the optimum temperature and release extra $CO_2$ into the air.
• In a laboratory, can be used to completely absorb from the air, proving that photosynthesis cannot occur without it (leading to a negative starch test).

Interpreting Limiting Factor Graphs

A graph of photosynthesis rate is like a diagnostic report telling you exactly what a plant needs most at any given moment.

• The linear phase (sloping up): The factor plotted on the x-axis is currently the limiting factor.
• The plateau (horizontal phase): The factor on the x-axis is no longer limiting the reaction; the rate is restricted by "something else" (either temperature or carbon dioxide).
• Temperature graphs are unique because they do not plateau at the top; instead, they form a bell-shaped curve because the rate rapidly crashes down to zero as enzymes denature.
• Sometimes, internal factors like a lack of chlorophyll (caused by magnesium deficiency or a viral infection) can prevent light absorption, creating an artificial plateau regardless of the external environment.