Analyze and Evaluate Scientific Explanations and Predictions

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MCAT Chemical and Physical Foundations of Biological Systems › Analyze and Evaluate Scientific Explanations and Predictions

Questions 1 - 10
1

A sealed syringe contains 10.0 mL of an ideal gas at 1.0 atm and 300 K. The plunger is pushed quickly to 5.0 mL, and the process is approximated as adiabatic. The student repeats the compression slowly and approximates it as isothermal. Which prediction is most consistent with thermodynamic principles for the final pressure in the fast (adiabatic) compression compared with the slow (isothermal) compression to the same final volume?

The adiabatic final pressure is higher, because temperature rises during adiabatic compression.

The final pressures are equal, because pressure depends only on volume for a fixed amount of gas.

The adiabatic final pressure is lower, because no heat enters to support increased pressure.

The isothermal final pressure is higher, because constant temperature implies greater kinetic energy after compression.

Explanation

This question tests the ability to evaluate predictions about adiabatic versus isothermal compression of ideal gases. The key principle is that adiabatic processes occur without heat exchange, so compression work increases internal energy and temperature, while isothermal processes maintain constant temperature through heat exchange. For the same volume reduction, adiabatic compression produces higher final pressure because both volume decrease and temperature increase contribute to pressure rise (PV^γ = constant, where γ > 1). In contrast, isothermal compression only has the volume effect (PV = constant at fixed T). Answer A correctly predicts higher adiabatic final pressure because temperature rises during adiabatic compression. Answer B incorrectly suggests lower pressure without heat input - this confuses the role of work versus heat in changing internal energy. To evaluate gas compression predictions, consider whether temperature changes (adiabatic) or remains constant (isothermal), then apply the appropriate relationship to predict final pressure.

2

A researcher tests whether dissolved CO$_2$ (aq) measurably acidifies water in a sealed 1.0 L vessel at 25°C. The vessel initially contains pure water equilibrated with 1.0 atm N$_2$ (no CO$_2$). The headspace gas is then replaced with 0.20 atm CO$_2$ (balance N$_2$) and allowed to re-equilibrate without changing temperature. Assume Henry’s law for CO$_2$: $\text{CO}2(\text{aq})=k_H P{\text{CO}_2}$ with $k_H=3.3\times10^{-2}$ M/atm, and that each dissolved CO$_2$ molecule contributes at most one H$^+$ via $\text{CO}_2+\text{H}_2\text{O}\rightleftharpoons \text{H}^+ + \text{HCO}_3^-$. Which prediction is most consistent with these principles regarding the final pH compared with the initial pH (7.0)?

It decreases only if the vessel is open to the atmosphere; in a sealed vessel pH cannot change.

It decreases, because increasing $P_{\text{CO}_2}$ increases $[\text{CO}_2(\text{aq})]$ and can increase $[\text{H}^+]$.

It is unchanged, because Henry’s law affects only gases, not aqueous equilibria.

It increases, because CO$_2$ is a base that consumes H$^+$ when dissolved.

Explanation

This question tests the ability to analyze and evaluate scientific predictions about pH changes when CO₂ dissolves in water. The key principle is that dissolved CO₂ forms carbonic acid through the equilibrium CO₂ + H₂O ⇌ H⁺ + HCO₃⁻, which releases H⁺ ions and lowers pH. In this sealed vessel system, Henry's law determines that [CO₂(aq)] = kH × PCO₂ = 3.3×10⁻² M/atm × 0.20 atm = 6.6×10⁻³ M. Since each dissolved CO₂ can contribute at most one H⁺, this increases [H⁺] and decreases pH below the initial 7.0. Answer A correctly predicts pH decreases because increasing PCO₂ increases dissolved CO₂ concentration, which increases H⁺ concentration. Answer B incorrectly claims CO₂ is a base - this is a common misconception confusing CO₂ with carbonate ions. To evaluate such predictions, check whether the dissolved species acts as an acid (releases H⁺) or base (consumes H⁺), then apply equilibrium principles to predict pH changes.

3

To evaluate a proposed mechanism for an enzyme assay, a student uses a buffer made from acetic acid/acetate. Two 10.0 mL samples are prepared at 25°C with identical total buffer concentration (0.10 M) but different ratios: Sample 1 has $\text{A}^-/\text{HA}=1$, Sample 2 has $\text{A}^-/\text{HA}=10$. The student adds 0.10 mL of 1.0 M HCl to each and assumes volume change is negligible. Given $pK_a(\text{acetic acid})=4.76$, which prediction is most consistent with the Henderson–Hasselbalch relationship for the direction and relative magnitude of pH change?

Both samples show the same pH decrease because total buffer concentration is identical.

Sample 1 shows a smaller pH decrease because it starts at higher pH and thus resists added acid better.

Sample 2 shows a larger pH decrease because higher initial pH implies weaker buffering against acids.

Sample 2 shows a smaller pH decrease because its larger initial $[\text{A}^-]$ better neutralizes added H$^+$.

Explanation

This question tests the ability to evaluate predictions about buffer capacity using the Henderson-Hasselbalch equation. The principle is that buffers resist pH changes best when they have substantial amounts of both the weak acid (HA) and conjugate base (A⁻) forms. Sample 1 has equal amounts ([A⁻]/[HA] = 1), while Sample 2 has ten times more base than acid ([A⁻]/[HA] = 10). When HCl is added, it provides H⁺ ions that react with A⁻ to form HA, consuming the base component. Sample 2, with its larger initial [A⁻], can neutralize more added H⁺ before depleting its base reserve, resulting in a smaller pH decrease. Answer C correctly identifies that Sample 2's larger [A⁻] better neutralizes added H⁺. Answer B incorrectly assumes identical total concentration means identical response - this ignores the importance of the ratio. To evaluate buffer predictions, consider which component (acid or base) reacts with the added species and whether sufficient amounts exist to neutralize it effectively.

4

A lab compares diffusion through a hydrated polymer film of thickness $L=1.0$ mm at 25°C. Under steady state, Fick’s first law is approximated as $J = D,\Delta C/L$, where $J$ is flux (mol·m$^{-2}$·s$^{-1}$), $D$ is diffusion coefficient, and $\Delta C$ is the concentration difference across the film. Trial A uses $\Delta C=0.10$ M; Trial B uses $\Delta C=0.20$ M. All else is identical. Which prediction is most consistent with the model for the ratio $J_B/J_A$?

$J_B/J_A = 1/2$, because higher concentration reduces the gradient by increasing collisions.

$J_B/J_A = 1$, because $D$ is constant and therefore flux is independent of $\Delta C$.

$J_B/J_A = 2$, because doubling $\Delta C$ doubles the driving force for diffusion.

$J_B/J_A = 4$, because flux scales with $(\Delta C)^2$ for steady-state diffusion.

Explanation

This question tests the ability to evaluate predictions using Fick's first law of diffusion. The fundamental principle is that diffusive flux J is directly proportional to the concentration gradient ΔC when other factors (D, L, temperature) remain constant: J = D × ΔC/L. In this system comparing two trials with identical conditions except concentration difference, Trial B has twice the concentration gradient of Trial A (0.20 M vs 0.10 M). Since flux is linearly proportional to ΔC, doubling the concentration difference doubles the flux, giving JB/JA = 2. Answer C correctly predicts this 2:1 ratio because doubling ΔC doubles the driving force. Answer D incorrectly suggests a quadratic relationship - this confusion may arise from other transport phenomena but doesn't apply to simple diffusion. When evaluating diffusion predictions, identify which variables change between conditions and apply the linear relationship J ∝ ΔC for constant D and L.

5

A student measures the electrical behavior of a cell suspension between two electrodes in a conductivity probe. The solution is modeled as an ohmic conductor with $R = \rho L/A$, where $\rho$ is resistivity, $L$ is electrode separation, and $A$ is electrode area. In a follow-up run, the student doubles both $L$ and $A$ while keeping ionic composition and temperature constant. Which prediction is most consistent with the model for the new resistance $R'$ relative to the original $R$?

$R' = R$, because doubling $L$ increases $R$ by 2 while doubling $A$ decreases $R$ by 2.

$R' = R/4$, because resistance decreases with both larger separation and larger area.

$R' = 2R$, because resistance depends only on separation, not on area.

$R' = 4R$, because both geometric changes increase resistance in series.

Explanation

This question tests the ability to evaluate predictions about electrical resistance using the relationship R = ρL/A. The key principle is understanding how resistance depends on geometry: it increases linearly with length L (more distance for current to travel) and decreases inversely with area A (more cross-sectional area for current flow). When both L and A are doubled while keeping resistivity ρ constant, the length effect (×2) and area effect (÷2) exactly cancel: R' = ρ(2L)/(2A) = ρL/A = R. Answer A correctly predicts R' = R because the two geometric changes have equal but opposite effects on resistance. Answer B incorrectly treats both changes as increasing resistance - this misunderstands that larger area decreases resistance. To evaluate such predictions, identify each variable's effect direction (increase or decrease) and magnitude, then combine multiplicatively for the overall change.

6

A researcher studies osmotic flow across a semipermeable membrane that passes water but not sucrose. Side 1 contains 0.10 M sucrose; Side 2 contains 0.20 M sucrose. Temperature is held at 298 K, and sucrose is treated as a non-electrolyte ($i=1$). The osmotic pressure difference is approximated by $\Delta\pi = iRT\Delta C$, with $R=0.082$ L·atm·mol$^{-1}$·K$^{-1}$. Which prediction is most consistent with the model for the direction of net water movement and the sign of $\Delta\pi$ (defined as $\pi_2-\pi_1$)?

Water moves from Side 2 to Side 1, and $\Delta\pi<0$.

Water moves from Side 1 to Side 2, and $\Delta\pi>0$.

No net water movement occurs because sucrose does not dissociate ($i=1$).

Water moves from Side 1 to Side 2, and $\Delta\pi<0$.

Explanation

This question tests the ability to evaluate predictions about osmotic flow using the osmotic pressure equation Δπ = iRTΔC. The fundamental principle is that water moves from regions of lower solute concentration (lower osmotic pressure) to higher concentration (higher osmotic pressure) across semipermeable membranes. With Side 1 at 0.10 M and Side 2 at 0.20 M sucrose, the concentration difference ΔC = 0.10 M creates an osmotic pressure difference Δπ = π₂ - π₁ = iRT(C₂ - C₁) > 0. Water moves from the dilute Side 1 to the concentrated Side 2 to equalize concentrations. Answer B correctly predicts water movement from Side 1 to Side 2 with Δπ > 0. Answer A reverses both the flow direction and sign - this is a common error confusing which side has higher pressure. To evaluate osmotic predictions, identify the concentration difference, calculate Δπ = iRTΔC, and remember water flows toward higher solute concentration.

7

A spectrophotometric assay uses Beer–Lambert law: $A = \varepsilon \ell c$. A dye has $\varepsilon=1.0\times10^4$ M$^{-1}$·cm$^{-1}$ at the measurement wavelength. In Trial 1, a 1.0 cm cuvette contains $c=10,\mu$M dye. In Trial 2, the dye concentration is unchanged but a 2.0 cm pathlength cuvette is used. Which prediction is most consistent with the model for the absorbance in Trial 2 relative to Trial 1?

It is unchanged, because absorbance depends on concentration only.

It doubles, because absorbance is proportional to pathlength at fixed $c$.

It is half, because a longer pathlength spreads light over a larger volume.

It quadruples, because absorbance is proportional to $\ell^2$.

Explanation

This question tests the ability to evaluate predictions using Beer-Lambert law A = εℓc. The key principle is that absorbance depends linearly on three factors: molar absorptivity ε (constant for a given compound and wavelength), pathlength ℓ, and concentration c. When only pathlength changes from 1.0 cm to 2.0 cm while keeping ε and c constant, absorbance doubles: A₂ = ε(2ℓ)c = 2(εℓc) = 2A₁. This makes physical sense - light travels through twice as much absorbing solution, encountering twice as many molecules. Answer C correctly predicts doubling because absorbance is proportional to pathlength at fixed concentration. Answer D incorrectly suggests a quadratic relationship - this confusion may arise from intensity relationships but doesn't apply to absorbance. To evaluate spectrophotometry predictions, identify which Beer-Lambert variables change and apply the direct proportionality A ∝ ℓ when ε and c are constant.

8

A team evaluates a claim that adding inert salt (NaCl) to an aqueous solution will increase the solubility of a sparingly soluble ionic compound MX(s) via “shielding.” They consider the dissolution equilibrium $\text{MX}(s)\rightleftharpoons \text{M}^+ + \text{X}^-$. The solubility product is defined in terms of activities: $K_{sp}=a_{\text{M}^+}a_{\text{X}^-}=\gamma_{\text{M}^+}\text{M}^+,\gamma_{\text{X}^-}\text{X}^-$. The team assumes adding NaCl increases ionic strength and decreases activity coefficients $\gamma$ for the ions. Which explanation is most plausible for how added NaCl can increase the measured molar solubility (concentration) of MX while $K_{sp}$ remains constant?

Lower $\gamma$ values allow higher ion concentrations while keeping the product of activities equal to $K_{sp}$.

Lower $\gamma$ values require lower ion concentrations to keep activities high enough to match $K_{sp}$.

NaCl decreases solubility because common ions always reduce dissolution, regardless of identity.

NaCl increases $K_{sp}$ by participating as a reactant in the dissolution equilibrium.

Explanation

This question tests the ability to evaluate explanations for ionic strength effects on solubility. The key principle is that solubility product Ksp is defined using activities (aM+ × aX-), which equal concentration times activity coefficient (γ[ion]). Adding inert salt increases ionic strength, which decreases activity coefficients γ below 1 through ion-atmosphere shielding effects. Since Ksp remains constant, lower γ values allow higher ion concentrations: if γ decreases, [M+] and [X-] must increase proportionally to maintain the same activity product. Answer A correctly explains that lower γ values permit higher concentrations while keeping the activity product equal to Ksp. Answer D reverses the logic - lower γ requires higher, not lower, concentrations to maintain constant activities. To evaluate ionic strength predictions, remember that Ksp = γM+[M+] × γX-[X-] stays constant, so decreasing γ allows increasing concentration.

9

A researcher measures the rate of a simple acid-catalyzed hydrolysis in water and proposes the rate law $\text{rate}=k\text{H}^+S$. Two buffered solutions at 25°C contain the same substrate concentration $S$ but different pH values: Solution X has pH 3.0 and Solution Y has pH 4.0. Assuming buffer components do not otherwise affect the reaction, which prediction is most consistent with the proposed rate law for the ratio $\text{rate}_X/\text{rate}_Y$?

$\text{rate}_X/\text{rate}_Y = 2$, because a 1-unit pH change doubles $[\text{H}^+]$.

$\text{rate}_X/\text{rate}_Y = 10$, because $[\text{H}^+]$ is 10-fold higher at pH 3 than at pH 4.

$\text{rate}_X/\text{rate}_Y = 1$, because pH affects equilibrium but not reaction rate.

$\text{rate}_X/\text{rate}_Y = 1/10$, because lower pH means fewer hydroxide ions to drive hydrolysis.

Explanation

This question tests the ability to evaluate predictions about pH effects on acid-catalyzed reaction rates. The key principle is that for reactions with rate = k[H+][S], the rate is directly proportional to hydrogen ion concentration. Since pH = -log[H+], a one-unit pH decrease represents a 10-fold increase in [H+]: at pH 3.0, [H+] = 10⁻³ M, while at pH 4.0, [H+] = 10⁻⁴ M. With identical substrate concentrations, the rate ratio equals the [H+] ratio: rateX/rateY = (10⁻³)/(10⁻⁴) = 10. Answer A correctly predicts a 10-fold ratio because [H+] is 10-fold higher at pH 3 than pH 4. Answer C incorrectly suggests only doubling - this misunderstands the logarithmic pH scale where each unit represents a 10-fold change. To evaluate pH-dependent rate predictions, convert pH differences to [H+] ratios using the 10-fold rule per pH unit, then apply the rate law proportionality.

10

A pulse of monochromatic light (wavelength $\lambda=500$ nm) is directed at a thin metal surface in vacuum to test the photoelectric effect. The measured stopping potential is $V_s=0.20$ V. Using $K_{max}=eV_s$ and photon energy $E=hc/\lambda$, the work function is estimated by $\phi=E-K_{max}$. Constants: $h=6.63\times10^{-34}$ J·s, $c=3.00\times10^8$ m/s, $e=1.60\times10^{-19}$ C. If the wavelength is decreased to 400 nm with all else unchanged, which prediction is most consistent with the model for the stopping potential?

It becomes negative, because higher photon energy reverses electron flow direction.

It is unchanged, because stopping potential depends only on the metal’s work function.

It increases, because photon energy increases as $\lambda$ decreases, increasing $K_{max}$.

It decreases, because shorter wavelength photons have less energy and eject slower electrons.

Explanation

This question tests the ability to evaluate predictions about the photoelectric effect using Einstein's model. The key principle is that photon energy E = hc/λ increases as wavelength decreases, and the maximum kinetic energy of ejected electrons equals photon energy minus work function: Kmax = E - φ = eVs. When wavelength decreases from 500 nm to 400 nm, photon energy increases from 2.48 eV to 3.10 eV (using E = 1240 eV·nm/λ). Since the work function φ remains constant for the same metal, the increased photon energy produces higher Kmax and thus higher stopping potential Vs. Answer B correctly predicts increased stopping potential because photon energy increases as λ decreases. Answer A incorrectly claims shorter wavelengths have less energy - this reverses the E ∝ 1/λ relationship. To evaluate photoelectric predictions, remember that decreasing wavelength means increasing photon energy, which increases the maximum kinetic energy and stopping potential for the same metal.

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