063 – The influence of concentration on reaction rate 1

Collecting the gas that a reaction gives off is one of the oldest ways of following its progress, and still one of the most direct: every millilitre that appears in the burette stands for a known number of molecules, so a graduated tube and a stopwatch are enough to turn a chemical change into a curve. The same measurement is used industrially wherever a gas is the product or the by-product of a process — hydrogen generation, fermentation, the anaerobic digestion of biomass, the curing of concrete — and in the analytical laboratory it is how carbonate content and the strength of an effervescent tablet are determined.

The rate of a reaction between a solid and a dissolved reagent is set at the surface where the two meet. Dissolved molecules arrive at that surface at a frequency proportional to how many of them there are per unit volume, so doubling the concentration of the acid roughly doubles the number of productive encounters each second. Concentration therefore changes how fast the reaction runs, but not how far it goes: the amount of product is fixed by whichever reagent runs out first, which here is always the magnesium.

In this laboratory you will build a water-filled gas burette inverted over a beaker, react about 0.2 g of magnesium powder with 150 mL of hydrochloric acid in a stirred Erlenmeyer flask, and read the volume of hydrogen collected every ten seconds. The run is repeated at three acid concentrations — 0.3, 0.2 and 0.5 mol/L — with the mass of magnesium held constant, so that the only variable is the strength of the acid. Comparing the three curves separates the two questions a kinetics experiment must always keep apart: how quickly the reaction goes, and how much it produces.

Educational Goals

Assembly and operation of a gas-collection apparatus

• Assemble a water-filled burette inverted over a reservoir, and recognise the signs that it has been filled or positioned incorrectly.
• Connect a reaction vessel to a collection tube through a two-hole stopper, a glass elbow and a plastic connector, and check that the path is closed before the reaction starts.

Stoichiometry and the gas laws

• Convert a mass of magnesium into a number of moles, and that number of moles into a volume of hydrogen at room conditions.
• Identify the limiting reagent in each of the three runs and predict the final volume before taking a single reading.

Chemical kinetics

• Explain how the concentration of a dissolved reagent governs the frequency of collisions at a solid surface, and therefore the rate.
• Distinguish the rate of a reaction from its extent, and say why changing the acid concentration alters one and not the other.

Quantitative measurement and graphing

• Take timed volume readings at a fixed interval and plot volume against time for the three runs on one set of axes.
• Obtain an initial rate from the slope of such a curve and state its units.

Interpretation of data

• Compare the three curves and decide whether they support a first-order dependence on the acid concentration.
• Name the corrections a gas burette calls for: the temperature of the gas, the water vapour saturating it, the head of water in the tube, and the delay between adding the metal and closing the flask.

Safety and waste handling

• Handle a dilute strong acid and a finely divided reactive metal with the appropriate protective equipment, and keep the hydrogen collected away from any source of ignition.
• Empty the spent mixture into the recovery beaker and rinse the glassware rather than discharging it to the sink.

Protocol

Assembly of the gas burette

1. Fill a 1 L beaker with at least 800 mL of tap water.
2. Place the 1 L beaker directly to the right of the hot plate.
3. Attach a universal clamp to the upper part of the stand above the center of the 1 L beaker, in order to support the gas burette.
4. Fill the 250 mL beaker with tap water.
5. Fill the gas burette to the brim with water from the 250 mL beaker.
6. Put a rubber stopper on the gas burette.
7. Secure the inverted gas burette to the clamp, so that the opening (end with the rubber stopper) is near the bottom of the 1 L beaker.
8. Remove the rubber stopper (the burette must be immersed in the beaker).

If water flows from the burette, it is because there is not enough water in the beaker or the burette is too high. If this is the case, restart steps 4 to 8.

9. Place the blue plastic connector so that its J-shaped opening is below the opening of the gas burette.

Measurement of the reaction

10. Place the Erlenmeyer flask on the hot plate. Do not turn on the heating element.
11. Insert the magnetic stir bar into the Erlenmeyer flask.
12. Pour 150 mL of 0.3 M hydrochloric acid (HCl) into the Erlenmeyer flask.
13. Using the spatula, take a small quantity of magnesium (Mg) powder and place it in the weighing boat in order to measure a quantity of approximately 0.2 g.
14. Deposit the powdered magnesium into the Erlenmeyer flask containing the hydrochloric acid solution.
15. Place the two-hole stopper, coupled to the glass elbow, on the Erlenmeyer flask.
16. Ensure that the glass elbow on the Erlenmeyer flask is aligned (connected) to the plastic connector attached to the gas burette.
17. Start the stopwatch.
18. Start the magnetic stirrer.
19. Take a reading of the gas volume in the burette every 10 seconds up to 2 minutes.

The results are also available in graphical form in the Results tab. / Volume vs. Time

20. After 2 minutes, stop the stopwatch and the magnetic stirrer.
21. Remove the stopper from the Erlenmeyer flask and remove the magnetic stirrer.
22. Remove the blue plastic connector from the burette.
23. Empty the contents of the Erlenmeyer flask into the recovery beaker and rinse it with distilled water.
24. Reset the stopwatch.
25. Restart steps 4 to 20 with the 0.2 M hydrochloric acid solution.
26. Restart steps 4 to 20 with the 0.5 M hydrochloric acid solution.

Note that the reaction is accelerated 10x.

Anticipated Outcomes

The reaction is the dissolution of magnesium metal in hydrochloric acid, which releases hydrogen: Mg(s) + 2 HCl(aq) → MgCl₂(aq) + H₂(g). One mole of metal gives one mole of gas, and the acid supplies two moles of hydronium ion for every mole of metal consumed.

How much gas: the same plateau in all three runs

The mass of magnesium is the same in every run, and in every run it is the limiting reagent, so all three curves must climb to the same final volume. With M(Mg) = 24.31 g/mol, a 0.2076 g sample is n = 0.2076 / 24.31 = 8.54 × 10⁻³ mol, and the equation gives the same number of moles of hydrogen. At 20 °C and 101.3 kPa the ideal-gas law gives V = nRT / P = (8.54 × 10⁻³ × 8.314 × 293) / 101 300 = 2.05 × 10⁻⁴ m³, that is 205 mL. Using the shorthand molar volume of 24 L/mol gives 205 mL as well, so the figure of 204 mL previously quoted on this page is the same number to the precision the measurement can support.

Each run consumes 2 × 8.54 × 10⁻³ = 1.71 × 10⁻² mol of hydrochloric acid. The 150 mL portions supply 0.0300, 0.0450 and 0.0750 mol at 0.2, 0.3 and 0.5 mol/L, so the acid is in excess by factors of 1.8, 2.6 and 4.4 and the magnesium is limiting throughout. This is the single most important point of the experiment and the one students most often miss: concentration changes the shape of the curve, not the height of its plateau.

How fast: the effect of concentration

For a solid dissolving in an acid the rate is proportional to the area of exposed metal and to some power of the hydronium-ion concentration: rate = k · A · [H₃O⁺]^a. The area is held fixed here by using the same mass of the same powder each time, so the ratio of the initial rates is the ratio of the concentrations raised to the power a. For magnesium in dilute hydrochloric acid a is close to one — the same order that laboratory 062 obtains for calcium carbonate — and a first-order law is the right starting hypothesis.

Taken at face value that predicts initial rates in the ratio 0.2 : 0.3 : 0.5, or 1.0 : 1.5 : 2.5. The acid is consumed as each run proceeds, however, and not equally: by the time the magnesium is gone the 0.2 mol/L solution has fallen to 0.086 mol/L, a loss of 57 %, while the 0.5 mol/L solution has fallen only to 0.386 mol/L, a loss of 23 %. The weakest acid slows down the most as it goes, so the completion times are spread further apart than the initial rates are. Using the mean of the initial and final concentrations as a rough stand-in for the whole run gives the figures below.

The expected ordering is therefore the one this page has always stated — 0.5 mol/L fastest, then 0.3, then 0.2 — but the measurement can say more than the ordering. If V_∞ is the plateau volume and V(t) the reading at time t, then V(t) / V_∞ is the fraction of the magnesium consumed, so the three runs can be replotted on a common vertical scale and compared directly. Taking the slope over the first twenty seconds, before the acid has been appreciably depleted, gives the initial rate in mL/s, and dividing by the molar volume converts it to mol/s. If those three initial rates stand in the ratio 1.0 : 1.5 : 2.5 the order in acid is one. If the ratio comes out flatter than that, the reaction is partly limited by the transport of acid to the metal surface rather than by the surface reaction itself, which is what happens at high concentration once every arriving ion reacts on contact.

Why the curves have the shape they do

Three things change together as a run proceeds and all three slow it down. The acid is consumed, by more than half in the weakest run. The magnesium particles shrink, so the area A in the rate law falls; for a powder whose grains dissolve at a constant linear speed the area falls roughly as the two-thirds power of the mass remaining, which is why the curve bends over well before the metal is gone. And the hydrogen produced clings to the metal as bubbles, masking part of the surface until stirring dislodges it — this is the reason the magnetic stirrer is not optional.

Working the other way is the heat of reaction. Taking Δ_rH ≈ −467 kJ per mole of magnesium, the figure used in laboratories 059 and 060, the 8.54 × 10⁻³ mol reacting here releases about 4.0 kJ. Delivered to 150 mL of solution, whose heat capacity is roughly 150 g × 4.18 J/(g·K) = 627 J/K, that is a temperature rise of about 6 °C if none of it escapes. With an activation energy of order 60 kJ/mol the Arrhenius factor for a rise from 293 K to 299 K is exp[(60 000 / 8.314)(1/293 − 1/299)] ≈ 1.6, so self-heating alone would speed the reaction up by about 60 % over the course of a run. Depletion and self-heating pull in opposite directions and the observed curve is the net of the two; the Erlenmeyer flask is not insulated, so in practice depletion wins and the curve flattens.

Reading the burette honestly

Three corrections separate the number on the burette from the amount of hydrogen collected. First, the gas in the tube stands over water and is saturated with water vapour, which at 20 °C contributes 2.3 kPa, or 2.3 % of atmospheric pressure. Second, the water inside the burette stands higher than the water in the beaker, and that column pushes back: a 20 cm head is ρgh = 1000 × 9.81 × 0.20 = 2.0 kPa, another 1.9 %. Both leave the collected gas at a pressure below atmospheric, so the volume read off is larger than the same quantity of hydrogen would occupy at 101.3 kPa — by about 4 % once the two are combined, which is well outside the reading error of the burette. Third, the conversion must use the temperature of the gas rather than an assumed 20 °C; a 5 °C error is 1.7 %. A class working to two significant figures may ignore all three. A class quoting three figures may not, and should apply P(H₂) = P(atmospheric) − P(water vapour) − ρgh before using the gas law.

Where this laboratory fits

This is one of a set of four experiments on the factors that govern reaction rate. Laboratories 061 and 062 hold the concentration fixed and vary the contact surface; this one and 064 hold the surface fixed and vary the concentration. Between them they isolate the two variables the collision model predicts should matter. Laboratory 062 in particular carries the determination of an order of reaction from a set of timed runs, which is the analysis these curves are best suited to, and laboratories 059 and 060 carry the calorimetry behind the enthalpy figure used above.

Summary of Assignment by Grade Range

Grade 9–10

Focus: What a reaction rate is, and the difference between how fast a reaction goes and how much it produces.

Activities: Assemble the burette and describe in words what happens when magnesium meets acid. Record the volume every ten seconds for each of the three concentrations and plot the three curves by hand on one grid. Answer two questions from the graph: which run reached 50 mL first, and did the three runs end at the same volume. Use the observation that they do to introduce the idea of a limiting reagent, and write the word equation for the reaction.

Grade 11

Focus: Quantitative treatment — stoichiometry, the ideal-gas law and the initial rate.

Activities: Balance the equation and calculate, before running anything, the moles of magnesium, the moles of hydrochloric acid supplied in each run and the volume of hydrogen expected at the measured room temperature. Confirm that the metal is limiting in all three. Measure the initial rate of each run from the slope of the first twenty seconds, express it in mL/s and in mol/s, and compare the three rates with the three concentrations. Record the temperature of the room and state what the answer would have been had it been 5 °C higher.

Grade 12 / College Level

Focus: Determination of the order of reaction, and an honest error budget.

Activities: Extract the initial rate of each run and fit ln(rate) against ln[HCl]; the slope is the order a in hydronium ion. Correct each burette reading for the water-vapour pressure and the hydrostatic head before converting it to moles. Account for the curvature of each trace using the shrinking-particle argument and the depletion of the acid, and estimate the temperature rise from the enthalpy of reaction to decide whether self-heating is large enough to matter. Compare the result with the order obtained for calcium carbonate in laboratory 062 and discuss why a diffusion-limited regime would flatten the apparent order.

Laboratory essentials

Instruments

• Beaker, 1000 mL (water reservoir for the inverted burette)
• Beaker, 500 mL (recovery of the spent mixture)
• Beaker, 250 mL (filling the burette)
• Electronic scale
• Erlenmeyer flask, 250 mL
• Gas burette, 200 mL
• Glass elbow with two-hole stopper
• Graduated cylinder, 250 mL
• Hot plate with magnetic stirrer (used as a stirrer only — the heating element stays off)
• Lab stand with universal clamp
• Magnetic stir bar
• Plastic connector (blue, J-shaped)
• Rubber stopper
• Spatula
• Thermometer
• Timer
• Weighing boat

Products

• HCl 0.2 mol/L (solution)
• HCl 0.3 mol/L (solution)
• HCl 0.5 mol/L (solution)
• Magnesium (powder, approximately 0.2 g per run)
• Distilled water (rinsing)
• Tap water