A group of students studied the decomposition of sodium bicarbonate (NaHCO_3) in aqueous s… — ACT

A group of students studied the decomposition of sodium bicarbonate ( $NaHCO_3$ ) in aqueous solution. They proposed a hypothesis: *The rate of $NaHCO_3$ decomposition increases as the initial concentration of $NaHCO_3$ increases because a higher concentration of reactant particles leads to more frequent collisions.*

To test this, they performed two experiments. In Experiment 1, they measured the volume of carbon dioxide ( $CO_2$ ) gas produced over $10\text{ min}$ at a constant temperature of $25^\circ\text{C}$ using different initial concentrations of $NaHCO_3$ ( $0.1\text{ M}$ , $0.2\text{ M}$ , and $0.3\text{ M}$ ). In Experiment 2, they repeated the trials at a constant temperature of $50^\circ\text{C}$ . The results are shown in the table:

Trial	Temperature ( $^\circ\text{C}$ )	Initial $NaHCO_3$ Concentration ( $\text{M}$ )	Total $CO_2$ Produced in $10\text{ min}$ ( $\text{mL}$ )
1	25	0.1	12.4
2	25	0.2	12.5
3	25	0.3	12.3
4	50	0.1	24.8
5	50	0.2	25.1
6	50	0.3	24.9

Which of the following statements best describes how the students should modify their hypothesis?

A
The students should retain their original hypothesis because the total volume of $CO_2$ gas produced increased when the temperature was raised from $25^\circ\text{C}$ to $50^\circ\text{C}$ .
The students should modify their hypothesis to state that the rate of $NaHCO_3$ decomposition is independent of the initial $NaHCO_3$ concentration but increases as temperature increases.Answer
C
The students should modify their hypothesis to state that the rate of $NaHCO_3$ decomposition increases as the initial $NaHCO_3$ concentration increases, but only at a constant temperature of $50^\circ\text{C}$ .
D
The students should modify their hypothesis to state that the rate of $NaHCO_3$ decomposition decreases as the initial $NaHCO_3$ concentration increases at higher temperatures.

Answer

The students should modify their hypothesis to state that the rate of

NaHCO_3

decomposition is independent of the initial

NaHCO_3

concentration but increases as temperature increases.

The experimental results demonstrate that changing the initial concentration of

NaHCO_3

from

0.1\text{ M}

0.3\text{ M}

has negligible effect on the volume of gas produced (remaining at approximately

12.4\text{ mL}

25^\circ\text{C}

and

25.0\text{ mL}

50^\circ\text{C}

). However, increasing the temperature from

25^\circ\text{C}

50^\circ\text{C}

significantly increases the rate of decomposition, doubling the gas output. Therefore, the hypothesis must be modified to state that the rate is independent of the initial concentration but increases with temperature.

Step-by-Step Solution

Analyze the effect of changing the initial

NaHCO_3

concentration at a constant temperature.

25^\circ\text{C}

(Trials 1-3), the

CO_2

volumes are

12.4\text{ mL}

12.5\text{ mL}

, and

12.3\text{ mL}

. At

50^\circ\text{C}

(Trials 4-6), the volumes are

24.8\text{ mL}

25.1\text{ mL}

, and

24.9\text{ mL}

To determine whether the data supports the students' hypothesis that a higher concentration increases the reaction rate.

Determine if there is a relationship between concentration and the rate of decomposition based on the step 1 results.

The volume of

CO_2

produced remains approximately constant regardless of the initial concentration, meaning concentration does not affect the rate.

To evaluate the validity of the original hypothesis.

Analyze the effect of temperature changes on the volume of gas produced at the same concentrations.

Comparing Trial 1 to Trial 4 (both

0.1\text{ M}

), the volume increases from

12.4\text{ mL}

24.8\text{ mL}

. Similar increases occur for other concentrations when temperature is raised.

To identify which variable (temperature) actually influences the rate of reaction.

Synthesize a modified hypothesis that aligns with both findings.

The modified hypothesis should state that the rate of decomposition is independent of the initial

NaHCO_3

concentration but increases as temperature increases.

To construct a hypothesis that accurately accounts for all observed trends in the experimental data.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

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