An environmental chemist studies the capture of carbon dioxide (CO_2) by a newly synthesiz… — ACT

An environmental chemist studies the capture of carbon dioxide ( $CO_2$ ) by a newly synthesized metal-organic framework (MOF) at different temperatures. The chemist proposes the following hypothesis:

*Hypothesis*: As the temperature of the system increases, the amount of $CO_2$ gas adsorbed by the MOF at any given pressure will increase, because the increased kinetic energy of the gas molecules will enhance their interaction with the MOF's pore surface.

The chemist measures the mass of $CO_2$ adsorbed per gram of MOF ( $m_{ads}$ , in $mg/g$ ) at three different temperatures across a range of pressures, as shown in the table below:

Pressure (bar)	$m_{ads}$ at $273\text{ K}$ (mg/g)	$m_{ads}$ at $298\text{ K}$ (mg/g)	$m_{ads}$ at $323\text{ K}$ (mg/g)
1.0	120	85	50
3.0	210	150	95
5.0	260	190	120
7.0	290	215	140
10.0	320	240	160

Based on the experimental results, which of the following describes how the hypothesis should be modified?

A
The hypothesis should be modified to state that as temperature increases, the amount of $CO_2$ adsorbed increases only at pressures below $5.0\text{ bar}$ .
B
The hypothesis should be retained as originally proposed, because the increase in pressure leads to an increase in $m_{ads}$ at all three temperatures tested.
The hypothesis should be modified to state that as temperature increases, the amount of $CO_2$ adsorbed decreases, indicating that the adsorption process is weakened by higher thermal energy.Answer
D
The hypothesis should be modified to state that at a pressure of $10.0\text{ bar}$ , a temperature of $350\text{ K}$ will result in a $m_{ads}$ value greater than $320\text{ mg/g}$ .

Answer

The hypothesis should be modified to state that as temperature increases, the amount of

CO_2

adsorbed decreases, indicating that the adsorption process is weakened by higher thermal energy.

The correct answer states that the hypothesis should be modified to show that adsorption decreases as temperature increases. Comparing the columns at any given pressure (horizontal rows) reveals that

m_{ads}

consistently drops as temperature rises from

273\text{ K}

323\text{ K}

. For instance, at

1.0\text{ bar}

, the adsorption goes from

120\text{ mg/g}

85\text{ mg/g}

and then to

50\text{ mg/g}

. This inverse relationship directly refutes the chemist's proposal that higher temperatures would increase adsorption, requiring a complete reversal of the hypothesized trend.

Step-by-Step Solution

Identify the variable relationships in the hypothesis.

The hypothesis predicts a direct relationship: increasing temperature increases the mass of gas adsorbed (

m_{ads}

) at any constant pressure.

To evaluate the hypothesis, we must first define the expected trend it predicts.

Analyze the experimental data for temperature effects at a constant pressure.

At a constant pressure of

5.0\text{ bar}

m_{ads}

260\text{ mg/g}

273\text{ K}

190\text{ mg/g}

298\text{ K}

, and

120\text{ mg/g}

323\text{ K}

. This represents an inverse relationship.

Comparing values across a single row isolates the effect of temperature on adsorption while keeping pressure constant.

Determine the necessary modification to the hypothesis.

Since the actual trend is opposite to the prediction (adsorption decreases as temperature increases), the hypothesis must be modified to reflect this inverse relationship.

Scientific hypotheses must be updated or discarded when they are contradicted by empirical data.

Key Concept

Formulating and Modifying Hypotheses

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic