Experimental Design and Scientific Method

Researchers investigated the leaching of calcium ions ($Ca^{2+}$) from sandy loam soil under simulated rainfall conditions. Six soil columns, each containing $500\text{ g}$ of soil, were prepared. The simulated rainfall rate was held constant at $50\text{ mL/hr}$ for $10\text{ hours}$. The leachate was collected and analyzed for total dissolved $Ca^{2+}$ concentration (in $\text{mg/L}$). The composition of each column and the pH of the simulated rainfall applied are summarized in the table below:

Which columns must be compared to address each research objective while isolating the single variable of interest? Match each research objective on the left with the correct column comparison on the right.

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To study the biodegradation of a synthetic polymer, polyethylene terephthalate (PET), by a newly isolated bacterium (*Thermobacillus petrolei*), researchers conducted two experiments.

In Experiment 1, five test tubes were prepared with $10\text{ mL}$ of a liquid nutrient medium, $50\text{ mg}$ of PET film, and $1.0\text{ mL}$ of an active *T. petrolei* suspension. The pH and temperature were kept constant. A different concentration of a synthetic surfactant, Surfactant X, was added to Tubes 1–4. Tube 5 did not receive Surfactant X. After 7 days, the remaining mass of PET was measured to evaluate degradation.

In Experiment 2, to determine whether the PET degradation observed in Experiment 1 was due to active bacterial metabolic activity rather than non-biological chemical hydrolysis or passive physical absorption onto the bacterial biomass, the researchers prepared four additional test tubes (Tubes 6–9) under the same environmental conditions as Experiment 1, but modified the tube contents as shown below:

To demonstrate that the degradation of PET film in Experiment 1 was specifically caused by the active metabolism of living *T. petrolei* cells rather than passive physical absorption of the polymer by the bacterial biomass, which of the following tubes from Experiment 2 serves as the most appropriate control when compared to Tube 5?

A biology lab group investigated how wind speed affects the rate of water loss in *Phaseolus vulgaris* (common bean) plants. The group initially hypothesized that transpiration rates would increase continuously and linearly across all wind speeds due to the constant removal of the boundary layer of water vapor.

They recorded the transpiration rates at different wind speeds in a wind tunnel and compiled the data in the table below:

Based on the results in the table, which of the following statements represents the most accurate modification of the group's initial hypothesis?

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:

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

A student proposed the following hypothesis regarding the behavior of crickets:

*Hypothesis*: As the surrounding temperature increases, the chirping rate of crickets will decrease because lower temperatures stimulate metabolic activity.

The student measured the chirping rate of a group of crickets at different temperatures and recorded the results in the table below:

Based on the data, how should the student modify the hypothesis?

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To study the biodegradation of polyethylene terephthalate (PET) by a newly engineered strain of *Pseudomonas putida*, researchers set up several liquid culture vessels containing a baseline mineral medium ($M9$), a fixed concentration of PET film ($0.5\%\text{ w/v}$), and varying combinations of additional factors. The strain normally requires a co-substrate, such as succinate, to support growth during PET degradation. The researchers tested the effects of adding $10\text{ mM}$ succinate, adding $50\text{ }\mu\text{M}$ of cadmium ($Cd^{2+}$, a heavy metal inhibitor), and incubating at different temperatures. Each vessel was inoculated with $10^6\text{ cells/mL}$ of *P. putida* and incubated for 7 days.

The setups for the groups are described in the table below:

The researchers measured the dry weight loss percentage of the PET film after 7 days to evaluate PET-degrading activity.

To isolate and determine the specific inhibitory effect of cadmium ($Cd^{2+}$) on PET biodegradation at the standard growth temperature of $30\text{ °C}$, the researchers must compare the PET weight loss of Group 3 to the PET weight loss of which of the following groups?

A student investigates the rate of an enzyme-catalyzed reaction. The student proposed the following hypothesis:

*Hypothesis*: The rate of the reaction is directly proportional to the enzyme concentration at all temperatures, meaning that doubling the enzyme concentration will double the reaction rate regardless of the temperature.

To test this hypothesis, the student measured the reaction rate (in $\mu\text{mol/min}$) at enzyme concentrations of $1.0\text{ g/L}$ and $2.0\text{ g/L}$ across four different temperatures. The results are shown in the table below:

Which of the following statements best explains whether the data support the student's hypothesis, and how the hypothesis should be modified?

To investigate the effect of wind speed on the rate of transpiration, students placed four identical oak saplings in potometers. Each sapling was exposed to a fan at a different distance to vary the wind speed, with Trial 4 serving as the control group (no fan). The trials were conducted sequentially inside a greenhouse, and the ambient temperature, relative humidity, and transpiration rate were recorded for each 1-hour trial. The results are shown in the table below.

Based on these results, the students concluded that a wind speed corresponding to a distance of $1.5\text{ m}$ from the fan maximizes the rate of transpiration in oak saplings. Which of the following statements identifies the primary flaw in this conclusion?

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An environmental scientist investigated the efficiency of sunflower plants (*Helianthus annuus*) in phytoremediation—the process of using living plants to remove heavy metals from contaminated soil. Sunflowers were grown in pots containing soil with a baseline lead ($Pb^{2+}$) concentration of $500\text{ mg/kg}$ under controlled greenhouse conditions. The scientist set up several experimental groups to evaluate how two soil amendments—biochar and arbuscular mycorrhizal fungi (AMF)—affect the rate of $Pb^{2+}$ uptake by the plants.

The experimental groups were designed as follows:
* Group A: Soil with $0\text{ mg/kg}$ of $Pb^{2+}$, no biochar, no AMF.
* Group B: Soil with $500\text{ mg/kg}$ of $Pb^{2+}$, no biochar, no AMF.
* Group C: Soil with $500\text{ mg/kg}$ of $Pb^{2+}$, biochar added ($5\%\text{ w/w}$), no AMF.
* Group D: Soil with $500\text{ mg/kg}$ of $Pb^{2+}$, no biochar, AMF added.
* Group E: Soil with $500\text{ mg/kg}$ of $Pb^{2+}$, biochar added ($5\%\text{ w/w}$), AMF added.

All groups were watered daily with $100\text{ mL}$ of distilled water and kept at a constant temperature of $24^\circ\text{C}$ under a $14\text{-hour}$ light/$10\text{-hour}$ dark cycle. After $6\text{ weeks}$, the dry biomass of the plants and the concentration of $Pb^{2+}$ in the plant tissues were measured.

To evaluate the specific influence of each experimental variable, the scientist must compare the results of a test group to a corresponding control or baseline group. Match each of the following experimental objectives with the group that serves as the most appropriate control or baseline.

A student wanted to test how temperature affects the rate of a chemical reaction between baking soda and vinegar. The student performed two trials:

* Trial 1: $10\text{ g}$ of baking soda was mixed with $50\text{ mL}$ of vinegar at $20^\circ\text{C}$ in a beaker, and the mixture was stirred.
* Trial 2: $10\text{ g}$ of baking soda was mixed with $50\text{ mL}$ of vinegar at $40^\circ\text{C}$ in an identical beaker, and the mixture was not stirred.

The reaction rate was determined by measuring the volume of carbon dioxide gas produced. Which of the following describes a flaw in this experimental design?

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A team of geobiologists investigated the role of the soil bacterium *Bacillus subtilis* and soil humic acids on the dissolution rate of calcite ($CaCO_3$), a common carbonate mineral. Five experimental trials were conducted at $25^\circ\text{C}$ for 14 days. In each trial, 10.0 grams of calcite was placed in a reaction vessel containing 500 mL of an aqueous solution. The dissolution rate was determined by measuring the cumulative concentration of calcium ions ($Ca^{2+}$) released into the solution. The experimental setups are detailed below:

* Trial 1: Sterile deionized water (pH $7.0$), no bacteria.
* Trial 2: Aqueous solution containing $10\text{ mg/L}$ of humic acids (pH $5.5$), no bacteria.
* Trial 3: Sterile deionized water (pH $7.0$) inoculated with $10^6\text{ cells/mL}$ of living *B. subtilis*.
* Trial 4: Aqueous solution containing $10\text{ mg/L}$ of humic acids (pH $5.5$) inoculated with $10^6\text{ cells/mL}$ of living *B. subtilis*.
* Trial 5: Aqueous solution containing $10\text{ mg/L}$ of humic acids (pH $5.5$) inoculated with $10^6\text{ cells/mL}$ of heat-killed *B. subtilis*.

To determine if the enhancement of calcite dissolution in the presence of humic acids is specifically driven by the active metabolic processes of living *B. subtilis* rather than the passive physical presence of bacterial cell structures, researchers must compare Trial 4 to a control group. Which trial serves as the most appropriate control group for this comparison, and why?

A geologist conducted an experiment to test the following hypothesis:

*Hypothesis*: Basalt rocks subjected to freeze-thaw cycles will experience a greater percentage loss in mass when saturated with water of lower salinity, because lower salinity water expands more upon freezing, exerting greater pressure within rock pores.

Identical basalt rock samples of the same initial mass were saturated with water of three different salinity levels: $0\text{ g/L}$ (freshwater), $15\text{ g/L}$ (brackish water), and $35\text{ g/L}$ (ocean water). The samples were then subjected to $50$ freeze-thaw cycles between $-10^\circ\text{C}$ and $20^\circ\text{C}$. The average percentage loss in mass for each group of samples was calculated and recorded in the table below:

Do the results of the experiment support the geologist's hypothesis?

An experiment is conducted to study how the concentration of dissolved oxygen in an aquarium affects the respiration rate of a specific fish species. A researcher predicts that if the dissolved oxygen concentration increases, the respiration rate (measured in gill flares per minute) of the fish will decrease. The table below displays the results:

Based on the table, does the experimental data support the researcher's prediction?

A student hypothesized that as the concentration of dissolved carbon dioxide ($\text{CO}_2$) in water increases, the pH of the solution will increase. To test this, the student bubbled different volumes of $\text{CO}_2$ gas into 100 mL samples of distilled water at $25^\circ\text{C}$ and measured the pH of each sample. The results are shown in the table below:

Based on these results, which of the following represents the most appropriate modification to the student's hypothesis?

A student proposed the following hypothesis regarding planetary atmospheres:

*Hypothesis*: The rate of atmospheric escape of a gas from a planet's atmosphere is determined solely by the planet's surface temperature, such that planets with higher surface temperatures will experience higher rates of escape for all gases, regardless of the gravity of the planet or the molar mass of the gas.

To test this hypothesis, scientists measured the escape rates of helium ($He$, molar mass $\approx 4\text{ g/mol}$) and xenon ($Xe$, molar mass $\approx 131\text{ g/mol}$) from three different planets. The surface temperature, surface gravity (measured in units of $g$, where $1\text{ }g = 9.8\text{ m/s}^2$), and escape rates of the gases are shown in the table below:

Based on these results, which of the following modifications to the student's hypothesis is best supported by the data?

A group of students investigated the catalytic decomposition of hydrogen peroxide ($H_2O_2$) into water and oxygen gas using yeast as a source of the enzyme catalase:

In Study 1, they mixed $10\text{ mL}$ of $3\%\ H_2O_2$ with $2\text{ mL}$ of a $5\%$ yeast suspension in a sealed flask at $20^\circ\text{C}$ and recorded the volume of $O_2$ gas collected in a gas syringe over 5 minutes. They repeated this procedure using $10\%$, $15\%$, and $20\%$ yeast suspensions.

In Study 2, they used a $10\%$ yeast suspension and repeated the procedure at temperatures of $10^\circ\text{C}$, $30^\circ\text{C}$, $40^\circ\text{C}$, and $50^\circ\text{C}$. The volume of $O_2$ collected at 5 minutes increased with temperature up to $40^\circ\text{C}$ but was extremely low at $50^\circ\text{C}$.

The students want to perform a follow-up experiment to determine if the low $O_2$ production at $50^\circ\text{C}$ is due to the permanent thermal denaturation of catalase, or if the enzyme is simply temporarily less active at $50^\circ\text{C}$ but remains functional when returned to a lower temperature. Which of the following procedures would best allow the students to test this hypothesis?

A group of students designed experiments to study yeast fermentation under various conditions. During their planning, they identified several procedural issues. Match each experimental procedure to the primary source of error or confounding variable it introduces.

A student proposed the following hypothesis regarding liquid evaporation:

*Hypothesis*: The rate of evaporation of a liquid is directly proportional to its boiling point because liquids with stronger intermolecular forces evaporate more rapidly at a constant temperature of $25^\circ\text{C}$.

To test this hypothesis, the student placed equal volumes of three different liquids in identical open beakers. The beakers were kept in a temperature-controlled room at $25^\circ\text{C}$ and $1\text{ atm}$ of pressure. The volume of liquid remaining in each beaker was measured over a $24$-hour period to determine the average evaporation rate. The boiling points and measured evaporation rates are shown in the table below.

Based on these results, which of the following statements best describes how the student should modify their hypothesis?

A student proposed the following hypothesis regarding electromagnetism:

*Hypothesis*: The magnetic field strength of an electromagnet, as measured by the number of steel paperclips it can lift, is directly proportional to the number of wire coils wrapped around its core.

To test this hypothesis, the student wrapped varying numbers of wire coils around an iron nail core, connected the coils to a constant power source, and recorded the average number of paperclips lifted over $5$ trials. The results are shown in the table below:

Which of the following modifications to the hypothesis is best supported by the experimental results?