Class 10 Biology: Photosynthesis Rate Numericals

This section tackles progressive numerical problems based on the rate of photosynthesis, focusing on oxygen evolution rates, the compensation point, and identifying limiting factors.

Essential Concepts & Formulas

Photosynthetic Equation: $6CO_2 + 12H_2O \underset{\text{Chlorophyll}}{\overset{\text{Sunlight}}{\longrightarrow}} C_6H_{12}O_6 + 6O_2 + 6H_2O$ (Note the specific conditions required for the reaction, represented above and below the arrow).
Rate of Photosynthesis: Calculated by measuring the oxygen ( $O_2$ ) evolution over time (e.g., bubbles per minute). $\text{Rate} = \frac{\text{Number of } O_2 \text{ Bubbles}}{\text{Time Taken}}$
Net vs. Gross Photosynthesis: Net Photosynthesis = Gross Photosynthesis - Respiration.

Visual Aid: The Hydrilla Experiment Setup

Setup Flow: [Light Source] ➔ (Distance 'd') ➔ [Beaker with Water] ➔ [Inverted Funnel] ➔ [Hydrilla Plant] ➔ (O₂ Bubbles) ➔ [Inverted Test Tube]

Problem 1: Basic Rate of Photosynthesis (Low Difficulty)

Question: During a laboratory experiment using the Hydrilla funnel setup, a student observes that 120 bubbles of oxygen are released over a period of 15 minutes under bright sunlight. Calculate the average rate of photosynthesis per minute.

Step-by-Step Solution:

Identify the Given Data:
- Total Oxygen Bubbles = $120$
- Total Time = $15 \text{ minutes}$
Apply the Rate Formula: $\text{Rate} = \frac{\text{Total Bubbles}}{\text{Total Time}}$
Calculation: $\text{Rate} = \frac{120}{15} = 8 \text{ bubbles/minute}$
Answer: The average rate of photosynthesis is $8 \text{ bubbles per minute}$ .

Problem 2: The Compensation Point (Medium Difficulty)

Question: A potted plant is kept in a closed glass bell jar. Sensors monitor the total $O_2$ and $CO_2$ levels inside the jar. At a specific low light intensity (at dawn), the sensors record that the net change in $CO_2$ concentration inside the jar is precisely zero. A student concludes: "Photosynthesis has completely stopped because there is no $CO_2$ uptake." Is the student correct? Justify your answer numerically using the concept of rates.

Common Pitfall: Students often confuse Net Photosynthesis with Gross Photosynthesis. They assume zero net change means zero metabolic activity.

Step-by-Step Solution:

Identify the biological processes: A plant simultaneously undergoes two processes:
- Photosynthesis (Gross): Consumes $CO_2$ , produces $O_2$ .
- Respiration: Consumes $O_2$ , produces $CO_2$ . (This occurs continuously, day and night).
Define Net Change: $\text{Net } CO_2 \text{ Uptake} = \text{Rate of Photosynthesis} - \text{Rate of Respiration}$
Analyze the scenario: The sensor shows Net $CO_2$ Change = 0. Therefore, $0 = \text{Rate of Photosynthesis} - \text{Rate of Respiration}$ $\text{Rate of Photosynthesis} = \text{Rate of Respiration}$
Conclusion: The student is incorrect. Photosynthesis has not stopped. Instead, it is occurring at the exact same rate as cellular respiration. The $CO_2$ released by respiration is immediately recycled and used for photosynthesis. This specific light intensity is known as the Compensation Point.

Problem 3: Light Distance and Percentage Drop (Medium-High Difficulty)

Question: When a desk lamp is placed at a distance of $10 \text{ cm}$ from a Hydrilla setup, the plant produces $40 \text{ bubbles/min}$ . When the lamp is moved further away to a distance of $30 \text{ cm}$ , the light intensity drops significantly, and the plant produces only $10 \text{ bubbles/min}$ . Calculate the percentage decrease in the rate of photosynthesis.

Step-by-Step Solution:

Identify the Given Rates:
- Initial Rate ( $R_1$ ) = $40 \text{ bubbles/min}$
- Final Rate ( $R_2$ ) = $10 \text{ bubbles/min}$
Calculate the Absolute Decrease: $\text{Decrease} = R_1 - R_2 = 40 - 10 = 30 \text{ bubbles/min}$
Calculate the Percentage Decrease: $\text{Percentage Decrease} = \left( \frac{\text{Decrease}}{\text{Initial Rate}} \right) \times 100$ $\text{Percentage Decrease} = \left( \frac{30}{40} \right) \times 100 = 0.75 \times 100 = 75\%$
Answer: The rate of photosynthesis decreased by $75\%$ when the light source was moved further away.

Problem 4: Identifying Rate Limiting Factors (High Difficulty)

Question: A tomato plant is grown in a greenhouse. At $20^\circ\text{C}$ and $0.03\% \text{ } CO_2$ , increasing the light intensity from $1000 \text{ lux}$ to $3000 \text{ lux}$ increases the photosynthetic rate from 15 to 45 units. However, increasing light intensity from $3000 \text{ lux}$ to $5000 \text{ lux}$ keeps the rate stagnant at 45 units. If the greenhouse temperature is then raised to $30^\circ\text{C}$ while keeping the light at $5000 \text{ lux}$ , the rate jumps to 60 units. Identify the limiting factor between 3000-5000 lux before the temperature was raised.

Identifying the Limiting Factor:

Increase Light

If Rate Increases ➔ Light is the Limiting Factor.

If Rate Does Not Increase ➔ Move to Step 2.

Increase Temp or CO₂

If Rate Increases ➔ Temp or CO₂ was the Limiting Factor.

If Rate Remains Stagnant ➔ Another Unknown Factor is Limiting.

Step-by-Step Solution:

Analyze Blackman's Law of Limiting Factors: If a process depends on multiple factors, its rate is limited by the pace of the slowest factor.
Examine Interval 1 (1000 to 3000 lux at $20^\circ\text{C}$ ): The rate increases proportionally as light increases. Light is the limiting factor here.
Examine Interval 2 (3000 to 5000 lux at $20^\circ\text{C}$ ): Light increases, but the rate is stagnant (45 units). The curve has plateaued. This means light is no longer limiting; there is enough light, but some other factor is holding the rate back.
Examine the change (Temperature increase to $30^\circ\text{C}$ at 5000 lux): Raising the temperature caused the rate to increase to 60 units. This proves that at $20^\circ\text{C}$ , the temperature was the bottleneck preventing the rate from going higher despite abundant light.
Answer: The limiting factor between 3000 and 5000 lux (at $20^\circ\text{C}$ ) was Temperature.

Class 10 Biology: Photosynthesis Rate Numericals

This section tackles progressive numerical problems based on the rate of photosynthesis, focusing on oxygen evolution rates, the compensation point, and identifying limiting factors.

Essential Concepts & Formulas

Photosynthetic Equation: $6CO_2 + 12H_2O \underset{\text{Chlorophyll}}{\overset{\text{Sunlight}}{\longrightarrow}} C_6H_{12}O_6 + 6O_2 + 6H_2O$ (Note the specific conditions required for the reaction, represented above and below the arrow).
Rate of Photosynthesis: Calculated by measuring the oxygen ( $O_2$ ) evolution over time (e.g., bubbles per minute). $\text{Rate} = \frac{\text{Number of } O_2 \text{ Bubbles}}{\text{Time Taken}}$
Net vs. Gross Photosynthesis: Net Photosynthesis = Gross Photosynthesis - Respiration.

Visual Aid: The Hydrilla Experiment Setup

Setup Flow: [Light Source] ➔ (Distance 'd') ➔ [Beaker with Water] ➔ [Inverted Funnel] ➔ [Hydrilla Plant] ➔ (O₂ Bubbles) ➔ [Inverted Test Tube]

Problem 1: Basic Rate of Photosynthesis (Low Difficulty)

Step-by-Step Solution:

Identify the Given Data:
- Total Oxygen Bubbles = $120$
- Total Time = $15 \text{ minutes}$
Apply the Rate Formula: $\text{Rate} = \frac{\text{Total Bubbles}}{\text{Total Time}}$
Calculation: $\text{Rate} = \frac{120}{15} = 8 \text{ bubbles/minute}$
Answer: The average rate of photosynthesis is $8 \text{ bubbles per minute}$ .

Problem 2: The Compensation Point (Medium Difficulty)

Common Pitfall: Students often confuse Net Photosynthesis with Gross Photosynthesis. They assume zero net change means zero metabolic activity.

Step-by-Step Solution:

Identify the biological processes: A plant simultaneously undergoes two processes:
- Photosynthesis (Gross): Consumes $CO_2$ , produces $O_2$ .
- Respiration: Consumes $O_2$ , produces $CO_2$ . (This occurs continuously, day and night).
Define Net Change: $\text{Net } CO_2 \text{ Uptake} = \text{Rate of Photosynthesis} - \text{Rate of Respiration}$
Analyze the scenario: The sensor shows Net $CO_2$ Change = 0. Therefore, $0 = \text{Rate of Photosynthesis} - \text{Rate of Respiration}$ $\text{Rate of Photosynthesis} = \text{Rate of Respiration}$
Conclusion: The student is incorrect. Photosynthesis has not stopped. Instead, it is occurring at the exact same rate as cellular respiration. The $CO_2$ released by respiration is immediately recycled and used for photosynthesis. This specific light intensity is known as the Compensation Point.

Problem 3: Light Distance and Percentage Drop (Medium-High Difficulty)

Step-by-Step Solution:

Identify the Given Rates:
- Initial Rate ( $R_1$ ) = $40 \text{ bubbles/min}$
- Final Rate ( $R_2$ ) = $10 \text{ bubbles/min}$
Calculate the Absolute Decrease: $\text{Decrease} = R_1 - R_2 = 40 - 10 = 30 \text{ bubbles/min}$
Calculate the Percentage Decrease: $\text{Percentage Decrease} = \left( \frac{\text{Decrease}}{\text{Initial Rate}} \right) \times 100$ $\text{Percentage Decrease} = \left( \frac{30}{40} \right) \times 100 = 0.75 \times 100 = 75\%$
Answer: The rate of photosynthesis decreased by $75\%$ when the light source was moved further away.

Problem 4: Identifying Rate Limiting Factors (High Difficulty)

Identifying the Limiting Factor:

Increase Light

If Rate Increases ➔ Light is the Limiting Factor.

If Rate Does Not Increase ➔ Move to Step 2.

Increase Temp or CO₂

If Rate Increases ➔ Temp or CO₂ was the Limiting Factor.

If Rate Remains Stagnant ➔ Another Unknown Factor is Limiting.

Step-by-Step Solution:

Analyze Blackman's Law of Limiting Factors: If a process depends on multiple factors, its rate is limited by the pace of the slowest factor.
Examine Interval 1 (1000 to 3000 lux at $20^\circ\text{C}$ ): The rate increases proportionally as light increases. Light is the limiting factor here.
Examine Interval 2 (3000 to 5000 lux at $20^\circ\text{C}$ ): Light increases, but the rate is stagnant (45 units). The curve has plateaued. This means light is no longer limiting; there is enough light, but some other factor is holding the rate back.
Examine the change (Temperature increase to $30^\circ\text{C}$ at 5000 lux): Raising the temperature caused the rate to increase to 60 units. This proves that at $20^\circ\text{C}$ , the temperature was the bottleneck preventing the rate from going higher despite abundant light.
Answer: The limiting factor between 3000 and 5000 lux (at $20^\circ\text{C}$ ) was Temperature.

Numerical Problems - Photosynthesis

Class 10 Biology: Photosynthesis Rate Numericals

Essential Concepts & Formulas

Visual Aid: The Hydrilla Experiment Setup

Problem 1: Basic Rate of Photosynthesis (Low Difficulty)

Problem 2: The Compensation Point (Medium Difficulty)

Problem 3: Light Distance and Percentage Drop (Medium-High Difficulty)

Problem 4: Identifying Rate Limiting Factors (High Difficulty)

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BioBot

Numerical Problems - Photosynthesis

Class 10 Biology: Photosynthesis Rate Numericals

Essential Concepts & Formulas

Visual Aid: The Hydrilla Experiment Setup

Problem 1: Basic Rate of Photosynthesis (Low Difficulty)

Problem 2: The Compensation Point (Medium Difficulty)

Problem 3: Light Distance and Percentage Drop (Medium-High Difficulty)

Problem 4: Identifying Rate Limiting Factors (High Difficulty)

On this page