Identifying Independent, Dependent, and Controlled Variables

A team of plasma physicists conducted an experiment to investigate electrical breakdown phenomena in synthetic atmospheric gas mixtures. In a sealed dielectric chamber, researchers systematically varied the volume ratio of nitrogen ($N_2$) to oxygen ($O_2$) across ten trials while recording the threshold breakdown voltage ($V_{bd}$) required to initiate a spark discharge. Throughout all experimental trials, the spacing between the two planar copper electrodes was fixed at $5.0\text{ mm}$, the total cell pressure was held constant at $101.3\text{ kPa}$, and the ambient temperature was maintained at $298\text{ K}$.

Match each experimental component from this investigation to its correct variable classification.

A student designs an experiment to test how different concentrations of salt water affect the germination rate of radish seeds. The student places 50 radish seeds in each of four petri dishes. Each dish is watered with a different concentration of salt solution ($0\%$, $1\%$, $2\%$, and $3\%$ salt). All petri dishes are kept in the same incubator at a constant temperature of $22^\circ\text{C}$ and receive 12 hours of light daily. After 5 days, the student counts the total number of germinated seeds in each dish. Match each experimental component on the left with its correct variable classification on the right.

A student conducted an experiment to determine how the temperature of a reactant solution affects the rate of a chemical reaction. The student placed equal volumes of $1.0\text{ M}$ hydrochloric acid ($\text{HCl}$) in five identical beakers. Each beaker was maintained at a different temperature ($10^\circ\text{C}$, $20^\circ\text{C}$, $30^\circ\text{C}$, $40^\circ\text{C}$, or $50^\circ\text{C}$). The student then added a $1.0\text{ g}$ strip of magnesium ribbon to each beaker and recorded the time it took for the magnesium ribbon to completely dissolve. Based on this description, which of the following was the independent variable in the experiment?

Researchers investigated the effect of light wavelength on the photosynthetic rate of *Elodea* plants. Over a 24-hour period, three identical setups were maintained at a constant temperature of $22^\circ\text{C}$ and exposed to different colors of light (red, blue, or green). The rate of photosynthesis was determined by measuring the volume of oxygen gas produced by the plants in milliliters.

Match each component of the experiment to the correct variable type it represents.

A student conducts an experiment to determine how the mass of a toy car affects the distance it travels after rolling down a ramp. The student releases cars of different masses ($50\text{ g}$, $100\text{ g}$, $150\text{ g}$, and $200\text{ g}$) from the same release height on the same ramp and measures the distance each car travels in meters. Which of the following is the independent variable in this experiment?

A marine biologist designs an experiment to investigate how varying the salinity of seawater affects the hatching rate of brine shrimp eggs. She places equal numbers of eggs into five separate tanks with different salt concentrations ($10$, $20$, $30$, $40$, and $50\text{ ppt}$). All tanks are maintained at a constant temperature of $22^\circ\text{C}$ and receive $12\text{ hours}$ of light daily. After $48\text{ hours}$, she records the percentage of hatched eggs in each tank. Match each experimental component on the left with its corresponding variable classification on the right.

A student designs an experiment to compare the sound-dampening ability of various insulation materials. Four identical wooden boxes are lined with a $2\text{ cm}$ layer of a different material: fiberglass, acoustic foam, cellulose, or mass-loaded vinyl. A sound generator inside each box plays a tone at a fixed intensity of $85\text{ dB}$. A decibel meter placed $1\text{ m}$ outside the box measures the remaining sound intensity. In this experiment, which of the following is the dependent variable?

A geology student conducts an experiment to test how the slope of a hill affects the rate of soil erosion. Four identical trays are filled with equal amounts of the same soil type. The trays are set at angles of incline of $10^\circ$, $20^\circ$, $30^\circ$, and $40^\circ$, respectively. Water is poured onto each tray at a constant rate for $5\text{ minutes}$, and the mass of soil washed away from each tray is collected and weighed.

In this experiment, which factor is the independent variable?

A physics student conducts an investigation to determine how the angle of tilt of a solar panel relative to the ground affects its electrical power output. The student tests the same solar panel at tilt angles of $0^\circ$, $15^\circ$, $30^\circ$, $45^\circ$, and $60^\circ$ under direct sunlight at 12:00 PM on a clear day, recording the power output in watts for each trial. What is the independent variable in this investigation?

An engineer conducts an experiment to investigate how varying the thickness of synthetic rubber padding affects the peak impact force absorbed during a collision test. In each trial, a $2.0\text{ kg}$ steel sphere is dropped from a constant height of $1.5\text{ m}$ onto padding samples measuring $5\text{ mm}$, $10\text{ mm}$, or $15\text{ mm}$ in thickness while maintaining the laboratory temperature at $20^\circ\text{C}$. Match each experimental component on the left with its corresponding variable classification on the right.

A team of biochemists investigated the activity of the enzyme *lactase* under varying pH conditions. Four test tubes were prepared, each containing $5.0\text{ mL}$ of a $2\%$ lactose substrate solution and $1.0\text{ mL}$ of standardized lactase solution. Buffer solutions were added to adjust the pH in the test tubes to 3.0, 5.0, 7.0, and 9.0, respectively. All test tubes were placed in a water bath maintained at a constant temperature of $37.0^\circ\text{C}$ for 15 minutes. The final concentration of glucose produced (measured in $\text{mg/dL}$) was determined for each test tube to quantify enzymatic activity.

Match each experimental component to its correct variable classification.

Biochemists investigated the catalytic activity of the enzyme carbonic anhydrase under various environmental conditions across three distinct experimental setups, as summarized in the table below.

Based on the experimental design shown for Trial 3, which of the following correctly identifies the independent variable, the dependent variable, and a key controlled variable, respectively?

Atmospheric researchers conducted an experiment inside a sealed environmental chamber maintained at a constant ambient temperature of $20.0^\circ\text{C}$ and a constant airflow velocity of $0.5\text{ m/s}$. The researchers adjusted the relative humidity ($RH$) across four distinct test runs ($40\%$, $50\%$, $60\%$, and $70\%$) while keeping the surface area and material of the condensing plate identical. After $60\text{ minutes}$ for each run, the total mass of condensed water on the plate surface was recorded.

Based on this experimental setup, which of the following correctly identifies the independent variable, the dependent variable, and one controlled variable in this investigation?

An atmospheric scientist conducts an experiment in a temperature-controlled environmental chamber to investigate the photolysis kinetics of nitryl chloride ($ClNO_2$) under varying moisture conditions. During the experiment, the scientist adjusts the initial atmospheric water vapor concentration ($H_2O$ mole fraction in ppmv) across five distinct trials while maintaining the total chamber pressure at $760\text{ Torr}$, ambient temperature at $298\text{ K}$, and UV actinic flux intensity at $1.5 \times 10^{16}\text{ photons}\cdot\text{cm}^{-2}\cdot\text{s}^{-1}$. For each trial, the scientist uses cavity ring-down spectroscopy to quantify the first-order photolysis rate constant ($k_{\text{phot}}$ in $\text{s}^{-1}$). Unintended background desorption of trace volatile organic compounds (VOCs) from the chamber walls occurs unpredictably between trials.

Match each experimental component described below to its correct variable classification.

A marine biology student designs an experiment to measure the rate of oxygen production in *Chlorella* algae. Four identical glass flasks are filled with equal volumes of an algal suspension of the same cell density. Each flask is exposed to a light source of a different wavelength (red, blue, green, and yellow) while keeping the light intensity fixed at $500\text{ lux}$ and the temperature constant at $22^\circ\text{C}$. The volume of dissolved oxygen produced by each culture is measured after $3\text{ hours}$.

Match each experimental element from this investigation to its corresponding variable type.

Researchers conducted a two-part investigation to evaluate the enzymatic degradation of polyethylene microplastics by a specialized bacterial strain (*Pseudomonas sp.*).

Experiment 1: Five identical culture flasks were filled with equal volumes of liquid mineral medium and $50.0\text{ mg}$ of standardized polyethylene film. Each flask was incubated at a different constant temperature ($20^\circ\text{C}$, $25^\circ\text{C}$, $30^\circ\text{C}$, $35^\circ\text{C}$, or $40^\circ\text{C}$) while maintaining a fixed agitation speed of $150\text{ rpm}$ and a constant $\text{pH}$ of $7.2$. After 14 days, the percentage mass loss of the polyethylene film was measured for each flask.

Experiment 2: Using the optimal incubation temperature identified in Experiment 1 ($35^\circ\text{C}$), five new flasks were prepared with identical initial media and $50.0\text{ mg}$ of polyethylene film. In this phase, the agitation speed was varied across the flasks ($50\text{ rpm}$, $100\text{ rpm}$, $150\text{ rpm}$, $200\text{ rpm}$, and $250\text{ rpm}$) while keeping temperature, $\text{pH}$, and incubation time constant. After 14 days, the percentage mass loss of the polyethylene film was measured.

Across both experiments, which of the following correctly categorizes the role of the $150\text{ rpm}$ agitation speed in Experiment 1 and the role of the percentage mass loss of polyethylene in Experiment 2?

A researcher conducts an experiment to determine how the drop height of a steel sphere affects the depth of the crater it creates when dropped into a tray of fine sand. In each trial, the same 50-gram steel sphere is dropped vertically from heights of 25 cm, 50 cm, 75 cm, and 100 cm into identical trays of dry sand, and the crater depth is measured immediately after impact. What is the independent variable in this experiment?

A group of environmental scientists conducted a study to evaluate how varying concentrations of dissolved oxygen ($2\text{ mg/L}$, $4\text{ mg/L}$, $6\text{ mg/L}$, and $8\text{ mg/L}$) in aquatic tanks affect the average swimming speed of juvenile rainbow trout (*Oncorhynchus mykiss*). In each trial, the water temperature was maintained at $15^\circ\text{C}$, the tank volume was held at $100\text{ L}$, and the photoperiod was fixed at 12 hours of light per day. Which of the following best identifies the independent variable in this experiment?

Biochemical engineers investigated the enzymatic degradation of polyethylene terephthalate (PET) microplastics using a newly isolated bacterial hydrolase.

Study 1
Four identical $250\text{ mL}$ reaction flasks were prepared, each containing $100\text{ mL}$ of a $50\text{ mg/L}$ PET microplastic suspension buffered at $\text{pH } 7.5$. To each flask, $0.10\text{ mg/mL}$ of hydrolase was added. The flasks were incubated for 24 hours at constant temperatures of $25^\circ\text{C}$, $35^\circ\text{C}$, $45^\circ\text{C}$, and $55^\circ\text{C}$, respectively, while continuously stirred at $200\text{ rpm}$. At the end of the 24-hour period, the mass loss of PET (in $\text{mg}$) in each flask was recorded.

Study 2
The procedure of Study 1 was repeated at a constant temperature of $45^\circ\text{C}$, but the enzyme concentration was varied across the four flasks ($0.05\text{ mg/mL}$, $0.10\text{ mg/mL}$, $0.15\text{ mg/mL}$, and $0.20\text{ mg/mL}$). PET mass loss was again measured after 24 hours.

In Study 1, which of the following correctly identifies the independent variable and the dependent variable?

A geochemist designed an experiment to evaluate the adsorption capacity of engineered biochar for lead ($Pb^{2+}$) ions in contaminated synthetic groundwater. In a series of experimental trials, the researcher systematically set the solution pH to different specific levels ($4.0$, $6.0$, and $8.0$) to observe its direct effect on heavy metal removal. After a $24$-hour equilibrium period, the scientist measured the final concentration of adsorbed $Pb^{2+}$ ions remaining on the biochar surface. Throughout all trials, the initial $Pb^{2+}$ concentration ($50\text{ mg/L}$), mass of biochar ($0.50\text{ g}$), vessel volume ($100\text{ mL}$), ambient temperature ($25^\circ\text{C}$), and agitation speed ($150\text{ rpm}$) were held strictly constant.

Match each experimental component listed on the left with its correct variable classification on the right.