Two students propose competing hypotheses regarding the rate of oxygen (O_2) gas productio… — ACT

Two students propose competing hypotheses regarding the rate of oxygen ( $O_2$ ) gas production during the catalytic decomposition of hydrogen peroxide ( $H_2O_2$ ) by a yeast suspension.

Student 1 Hypothesizes: The rate of $O_2$ production is directly proportional to the initial concentration of $H_2O_2$ because a higher concentration of reactant increases the frequency of collisions.

Student 2 Hypothesizes: The rate of $O_2$ production is limited by the number of active enzyme sites on the yeast cells. Once all active sites are saturated, the rate will reach a maximum value ( $V_{max}$ ) and remain constant, regardless of further increases in $H_2O_2$ concentration.

The students perform five trials measuring the volume of $O_2$ gas produced in the first 60 seconds under various initial conditions. The results are shown in the table below:

Trial	Initial $H_2O_2$ concentration (M)	Yeast suspension volume (mL)	Volume of $O_2$ produced in 60 s (mL)
1	0.5	2.0	15.0
2	1.0	2.0	30.0
3	2.0	2.0	45.0
4	3.0	2.0	45.0
5	2.0	4.0	90.0

Based on these results, which of the following statements best describes how one of the hypotheses should be modified to align with the experimental data?

Student 2's hypothesis is supported by the data, but it must be modified to state that the value of $V_{max}$ is directly proportional to the volume of the yeast suspension.Cevap
B
Student 1's hypothesis is supported by the data, but it must be modified to state that the rate of $O_2$ production decreases at yeast suspension volumes greater than 2.0 mL.
C
Student 2's hypothesis is refuted by the data, and it must be modified to state that yeast concentration has no effect on the maximum rate of reaction.
D
Student 1's hypothesis is supported across all trials, and it must be modified to state that doubling the concentration of $H_2O_2$ always results in a 1.5-fold increase in the volume of $O_2$ produced.

Cevap

Student 2's hypothesis is supported by the data, but it must be modified to state that the value of

V_{max}

is directly proportional to the volume of the yeast suspension.

The correct answer is the option stating that Student 2's hypothesis is supported but must be modified to show that the maximum rate is directly proportional to the volume of the yeast suspension. Trials 3 and 4 show that once a concentration of

2.0\text{ M}

is reached, further increases in

H_2O_2

do not increase the volume of

O_2

produced, confirming the saturation model. Trial 5 shows that doubling the yeast volume at this saturation level doubles the total

O_2

produced, confirming that

V_{max}

is directly proportional to the amount of catalyst.

Adım Adım Çözüm

Analyze Trials 3 and 4 to evaluate the effect of reactant concentration at high levels.

In Trials 3 and 4, the initial concentration of

H_2O_2

increases from

2.0\text{ M}

3.0\text{ M}

while yeast volume remains constant at

2.0\text{ mL}

. The volume of

O_2

produced remains constant at

45.0\text{ mL}

This identifies that the reaction rate has reached a plateau, which supports the active-site saturation hypothesis of Student 2.

Analyze Trial 5 relative to Trial 3 to determine the effect of catalyst volume.

In Trial 5, the yeast suspension volume is doubled to

4.0\text{ mL}

while keeping

H_2O_2

2.0\text{ M}

. The volume of

O_2

produced doubles from

45.0\text{ mL}

90.0\text{ mL}

This determines how the maximum rate (

V_{max}

) responds to an increase in enzyme concentration.

Synthesize the findings to modify the appropriate hypothesis.

Since

V_{max}

scales linearly with the yeast volume (from

45.0\text{ mL}

90.0\text{ mL}

when yeast volume doubles), Student 2's hypothesis must be modified to reflect that the maximum rate is directly proportional to catalyst volume.

This completes the formulation and modification of the hypothesis based on the entire dataset.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:1m 30s

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