IGCSE Chemistry 0620: Collision Theory for Concentration and Surface Area

Two students each investigate a different factor affecting the rate of reaction between magnesium metal and dilute hydrochloric acid, which produces hydrogen gas: $\text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g)$

Student A compares using $1.0\text{ mol/dm}^3$ hydrochloric acid with $2.0\text{ mol/dm}^3$ hydrochloric acid. The same volume of acid and the same mass and form of magnesium (a single ribbon) are used in both trials, and the acid is in excess in both cases.
Student B compares using $1.0\text{ g}$ of magnesium as a single ribbon with $1.0\text{ g}$ of magnesium as a powder. The same volume and concentration of hydrochloric acid is used in both trials, and the acid is in excess in both cases.

(a) Explain, using collision theory, why Student A's trial with $2.0\text{ mol/dm}^3$ acid has a greater initial rate of reaction than the trial with $1.0\text{ mol/dm}^3$ acid. Refer to the number of particles per unit volume in your answer. [3]

(b) Explain, using collision theory, why Student B's trial using magnesium powder has a greater initial rate of reaction than the trial using a single ribbon. [3]

(c) For each student's investigation, state whether the factor being changed affects the total volume of hydrogen gas eventually collected, given that the acid is in excess in every trial. [2]

Part (a): Explaining the effect of concentration

Hydrochloric acid at $2.0\text{ mol/dm}^3$ contains twice as many acid particles in each cubic decimetre of solution as acid at $1.0\text{ mol/dm}^3$ , because concentration is a direct measure of the number of particles per unit volume.

With more acid particles packed into the same volume of solution, the particles are, on average, closer together and closer to the surface of the magnesium ribbon. This means acid particles collide with magnesium atoms more frequently in the more concentrated trial.

Since the reaction between magnesium and hydrochloric acid can only occur where an acid particle collides with a magnesium atom, a higher frequency of collisions per second gives more successful collisions per second, so Student A’s $2.0\text{ mol/dm}^3$ trial has a greater initial rate of reaction.

Part (b): Explaining the effect of surface area

The $1.0\text{ g}$ of magnesium is exactly the same mass in both of Student B’s trials, but it is arranged very differently: as one solid ribbon, or as many tiny particles of powder. Splitting the same mass into powder creates a much greater total surface area exposed to the acid, because a much larger fraction of the magnesium’s atoms now lie at an outer, reacting surface rather than being “buried” inside a single solid strip.

With more magnesium surface exposed, acid particles are able to reach and collide with magnesium atoms more frequently in the powder trial than in the ribbon trial. More frequent collisions per second give more successful collisions per second, so the powdered-magnesium trial has a greater initial rate of reaction.

Part (c): Effect on the total volume of gas

In each investigation, only one thing differs between the two trials (concentration for Student A, particle size for Student B) while the mass of magnesium used and the fact that the acid is in excess stay the same in every trial. Since the acid is always in excess, magnesium is the limiting reactant in all four trials, and the same mass of magnesium always corresponds to the same fixed number of moles of magnesium.

Because the total amount of hydrogen gas produced depends only on the number of moles of the limiting reactant (magnesium), and this is identical within each student’s pair of trials, the total volume of hydrogen gas eventually collected is the same for both of Student A’s trials, and the same for both of Student B’s trials. Concentration and surface area each change only the rate at which this fixed total volume is reached, not the total volume itself.

Final answers

(a) Doubling concentration doubles the number of acid particles per unit volume $\Rightarrow$ more frequent collisions with magnesium $\Rightarrow$ faster initial rate.
(b) Powder has a far greater total surface area than a ribbon of the same mass $\Rightarrow$ more frequent collisions with acid particles $\Rightarrow$ faster initial rate.
(c) Neither factor changes the total volume of gas produced: the same mass (moles) of magnesium and excess acid are used in every trial, so only the rate differs.