--- title: "Kinetics: How Long Will That Marble Statue Last? - AP Chemistry Required Lab Guide" description: "Review Kinetics: How Long Will That Marble Statue Last? for AP Chemistry with CED-aligned concepts, lab skills, data analysis, and AP exam connections." canonical: "https://fiveable.me/ap-chem/required-labs/kinetics-marble-statue/study-guide/80aFqDJepcWb182UmG8e" type: "study-guide" subject: "AP Chemistry" unit: "Required Labs" lastUpdated: "2026-06-17" --- # Kinetics: How Long Will That Marble Statue Last? - AP Chemistry Required Lab Guide ## Summary Review Kinetics: How Long Will That Marble Statue Last? for AP Chemistry with CED-aligned concepts, lab skills, data analysis, and AP exam connections. ## Guide # Kinetics Lab: How Long Will That Marble Statue Last? This lab uses a real-world question (how fast does acid dissolve marble?) to get you practicing the core skills of chemical [kinetics](/ap-chem/unit-5/reaction-rates/study-guide/4V94d3BwjoPaOOyQtDKQ "fv-autolink"): measuring reaction rates, identifying what variables affect those rates, and using data to figure out the mathematical relationship between [concentration](/ap-chem/unit-3/beer-lambert-law/study-guide/smCHzraorVz6qlWW1oeB "fv-autolink") and time. ## Why This Lab Matters for the AP Exam Kinetics is one of the most calculation-heavy units in [AP Chemistry](/ap-chem "fv-autolink"), and the exam will absolutely ask you to interpret concentration-time graphs, write rate laws, and calculate rate constants. This lab gives you hands-on experience with exactly those skills. You are not just watching a reaction happen. You are collecting data, transforming it, and using it to make a mathematical argument about how the reaction behaves. That process is the heart of what the AP exam tests in [Unit 5](/ap-chem/unit-5 "fv-autolink"). ## CED Connections This lab connects directly to Topics 5.1, 5.2, and 5.3 in the AP Chemistry Course and Exam Description. **Topic 5.1 (Reaction Rates, LO 5.1.A):** The lab asks you to explain how experimental parameters like concentration, [surface area](/ap-chem/key-terms/surface-area "fv-autolink"), and temperature affect reaction rate. Essential knowledge 5.1.A.3 is basically the backbone of the whole investigation. **[Topic 5.2](/ap-chem/unit-5/intro-rate-law/study-guide/oq5mJS35IadrTLHLjdqZ "fv-autolink") (Introduction to Rate Law, LO 5.2.A):** You use initial rate data to determine the [order of the reaction](/ap-chem/key-terms/order-of-the-reaction "fv-autolink") with respect to each reactant and write a rate law expression. This maps directly to EK 5.2.A.2 through 5.2.A.5. **Topic 5.3 (Concentration Changes Over Time, LO 5.3.A):** You analyze concentration-time data by making multiple graphs (linear, ln, and reciprocal) to identify the [reaction order](/ap-chem/key-terms/reaction-order "fv-autolink") and calculate the **[rate constant](/ap-chem/key-terms/rate-constant "fv-autolink")**. EK 5.3.A.1 through 5.3.A.5 all show up here. ## What You Need to Be Able to Do These are the concrete skills this lab builds. If you can do all of these, you are in great shape for the exam. - **Identify variables:** State which variable you are changing (independent), what you are measuring (dependent), and what you are holding constant (controlled variables). - **Collect rate data:** Measure how a quantity related to the reaction (like mass lost, gas produced, or color change) changes over time. - **Compare initial rates:** Use the method of initial rates to figure out how changing concentration affects the rate, and from that determine **reaction order**. - **Make linearizing graphs:** Plot [A] vs. time, ln[A] vs. time, and 1/[A] vs. time to figure out which one gives a straight line. That straight line tells you the order. - **Calculate the rate constant k:** Pull the slope from your best linear graph and use it to find k, including the correct units. - **Calculate [half-life](/ap-chem/key-terms/half-life "fv-autolink"):** Use $$t_{1/2} = \frac{0.693}{k}$$ for a [first-order reaction](/ap-chem/key-terms/first-order-reaction "fv-autolink") and connect it back to the real-world question about how long a marble statue survives. - **Write a complete rate law:** Combine your order and [k value](/ap-chem/key-terms/k-value "fv-autolink") into a rate law expression. - **Construct a claim-evidence-reasoning (CER) argument:** Use your data as evidence to support a claim about how a variable affects reaction rate. ## Core Concepts ### Reaction Rate **Reaction rate** is how fast [reactants](/ap-chem/key-terms/reactants "fv-autolink") are converted into [products](/ap-chem/key-terms/products "fv-autolink") per unit of time. The units are mol/L/s (or mol·L-1·s-1). In this lab, the reaction is marble (calcium carbonate, CaCO3) dissolving in acid: $$\text{CaCO}_3(s) + 2\text{HCl}(aq) \rightarrow \text{CaCl}_2(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g)$$ You can track the rate by measuring how much CO2 is produced, how much mass is lost, or how the acid concentration drops over time. ### Rate Law and Reaction Order The **rate law** (also called the differential rate law) expresses the rate as a function of reactant concentrations: $$\text{rate} = k[\text{A}]^m[\text{B}]^n$$ The exponents m and n are the **reaction orders** with respect to each reactant. They are determined experimentally, not from the [balanced equation](/ap-chem/key-terms/balanced-equation "fv-autolink"). The sum m + n is the **overall order of the reaction**. - A **zero-order reaction** means the rate does not depend on concentration at all. - A **first-order reaction** means doubling the concentration doubles the rate. - A **[second-order reaction](/ap-chem/key-terms/second-order-reaction "fv-autolink")** means doubling the concentration quadruples the rate. ### Rate Constant The **rate constant (k)** is the proportionality constant in the rate law. Its value depends on temperature, and its units depend on the overall reaction order. For a first-order reaction, k has units of s-1. For a second-order reaction, k has units of M-1·s-1. ### Integrated Rate Laws The **[integrated rate law](/ap-chem/key-terms/integrated-rate-law "fv-autolink")** connects concentration to time mathematically. There is a different version for each reaction order: | Order | Integrated Rate Law | Linear Plot | Slope | |-------|-------------------|-------------|-------| | Zero | $$[\text{A}]_t = [\text{A}]_0 - kt$$ | [A] vs. t | -k | | First | $$\ln[\text{A}]_t = \ln[\text{A}]_0 - kt$$ | ln[A] vs. t | -k | | Second | $$\frac{1}{[\text{A}]_t} = \frac{1}{[\text{A}]_0} + kt$$ | 1/[A] vs. t | +k | ### Half-Life **Half-life (t1/2)** is the time it takes for the concentration of a reactant to drop to half its starting value. For a **first-order reaction**, the half-life is constant regardless of starting concentration: $$t_{1/2} = \frac{0.693}{k}$$ This is a big deal. It means you can predict how long it takes for the marble to lose half its mass to acid weathering, which is exactly the real-world question this lab is built around. [Radioactive decay](/ap-chem/key-terms/radioactive-decay "fv-autolink") is another classic first-order process, and the AP exam loves to connect these two contexts. ### Factors That Affect Reaction Rate Three factors come up directly in this lab: - **Concentration:** Higher concentration of acid means more frequent collisions between H+ ions and the marble surface, so the rate increases. - **Surface area:** Breaking marble into smaller pieces exposes more surface to the acid. More contact points means faster reaction. This is why a marble statue weathers faster if it is cracked or chipped. - **[Catalysts](/ap-chem/key-terms/catalyst "fv-autolink"):** A **catalyst** speeds up a reaction by providing an alternative pathway with lower activation energy. It is not consumed in the reaction. In this lab, you might explore whether temperature or other factors mimic this effect, but the surface area and concentration variables are the main focus. ## How the Lab Works The central question is: what factors control how fast acid eats away at marble, and can we model that mathematically? You are essentially modeling acid rain weathering a marble statue. The marble is CaCO3, and the acid (typically HCl in lab settings) represents the acidic environment. As the reaction proceeds, the marble dissolves and CO2 gas is released. The investigation has two main parts. **Part 1: Identifying variables that affect rate.** You change one variable at a time (concentration of acid, surface area of marble, or temperature) while holding everything else constant. By comparing how fast the reaction runs under different conditions, you build evidence for which variables matter and how much. **Part 2: Determining the rate law.** You collect concentration-time data for the acid and then test three different graph transformations to figure out the reaction order. Whichever transformation gives you a straight line tells you the order. From the slope of that line, you calculate k. Then you can write the full rate law and calculate the half-life. The guided-inquiry piece means you are not just following a recipe. You will likely be asked to design part of the experiment yourself, choose which variables to test, and justify your choices. ## Data and Analysis Moves ### Controlling Variables Every trial where you change concentration should keep surface area and temperature constant. Every trial where you change surface area should keep concentration and temperature constant. If you change two things at once, you cannot tell which one caused the change in rate. ### Method of Initial Rates To find reaction order from initial rate data, compare two trials where only one concentration changes. If doubling [HCl] doubles the rate, the reaction is first order in HCl. If doubling [HCl] quadruples the rate, it is second order. Mathematically: $$\frac{\text{rate}_2}{\text{rate}_1} = \left(\frac{[\text{A}]_2}{[\text{A}]_1}\right)^m$$ Solve for m by taking the log of both sides if the ratio is not an obvious integer. ### Graphical Analysis for Reaction Order Take your concentration-time data and make all three plots: 1. [A] vs. time 2. ln[A] vs. time 3. 1/[A] vs. time The one that is most linear (closest to a straight line, highest R2 value) tells you the order. Then use the slope of that line to find k. Remember: for a first-order plot, slope = -k, so k is positive. ### Calculating Half-Life Once you have k for a first-order reaction, plug it into: $$t_{1/2} = \frac{0.693}{k}$$ You can then use this to make a real-world prediction. If k = 0.0035 s-1, then t1/2 is about 198 seconds. Scale that up to geological time and you can estimate how long a marble statue would last under constant acid exposure. ### Units Check Always check your units on k. If your rate is in mol/L/s and your concentration is in mol/L: - Zero order: k has units of mol·L-1·s-1 - First order: k has units of s-1 - Second order: k has units of L·mol-1·s-1 (or M-1·s-1) Getting the units wrong is a common point loss on the AP exam. ### Error Considerations When comparing trials, think about sources of error that could affect your results: - Inconsistent marble piece sizes when testing surface area - Temperature fluctuations during the experiment - Timing errors at the start of the reaction - CO2 escaping before you can measure it Acknowledging these in your analysis and explaining how they would affect your calculated rate or k value is exactly what the AP exam expects in a free-response question. ## Common Mistakes **Confusing reaction order with stoichiometric coefficients.** The exponents in the rate law come from experiment, not from the balanced equation. The coefficient of HCl in the balanced equation is 2, but that does not mean the reaction is second order in HCl. Do not make this assumption. **Forgetting that k changes with temperature.** The rate constant k is only constant at a fixed temperature. If you run trials at different temperatures, you will get different k values. That is expected and correct. **Misreading the slope sign.** For a first-order reaction, the slope of ln[A] vs. time is -k. The slope is negative, but k itself is a positive number. Do not report a negative rate constant. **Assuming first order without checking.** Just because the half-life concept is the most famous part of this topic does not mean every reaction in this lab is first order. Make all three graphs and let the data tell you the order. **Mixing up half-life formulas.** The simple formula $$t_{1/2} = 0.693/k$$ only applies to first-order reactions. Second-order half-life depends on initial concentration. The AP exam will test whether you know the difference. **Ignoring surface area as a kinetics variable.** Surface area affects rate but does not appear in the rate law expression (because the marble is a solid and solids are not included in rate laws). Students sometimes confuse "affects the rate" with "appears in the rate law." These are different things. **Sloppy CER writing.** On the AP exam, a claim without specific numerical evidence from your data will not earn full credit. Do not just say "increasing concentration increased the rate." Say by how much, and connect it to the mathematical relationship you found. ## Quick Review Checklist - You can explain how concentration, surface area, and temperature each affect reaction rate and why (in terms of [collision frequency](/ap-chem/unit-3/solids-liquids-gases/study-guide/uNMmoAyjJQkL63ysUrJC "fv-autolink") and energy). - You can use the method of initial rates to determine reaction order with respect to each reactant and write the full rate law. - You know which graph to make for each reaction order ([A] vs. t for zero, ln[A] vs. t for first, 1/[A] vs. t for second) and how to get k from the slope. - You can calculate the rate constant k with correct units for zero, first, and second order reactions. - You can calculate half-life for a first-order reaction using $$t_{1/2} = 0.693/k$$ and explain why half-life is constant for first-order processes. - You understand that reaction order is determined experimentally and cannot be read from the balanced equation. - You can connect first-order kinetics to real-world contexts like marble weathering and radioactive decay. - You can write a complete CER response using specific numerical data from the lab as evidence.