Mechanism for reaction between hydrochloric acid and magnesium

Question

Balanced equation:

$$\ce{Mg(s) + 2HCl(aq) -> MgCl2(aq) + H2(g)}$$

However, Cl^- is a spectator ion so the actual reaction equation is:

$$\ce{Mg + 2H+ -> Mg^2+ + H2}$$

Here is my proposed reaction mechanism:

1. A magnesium atom reacts with a $\ce{H+}$ ion: $\ce{Mg + H+ -> Mg+ + H}$

2. The $\ce{Mg+}$ intermediate produced reacts with another $\ce{H+}$ ion: $\ce{Mg+ + H+ -> Mg^2+ + H}$

3. The two hydrogen atoms (from step 1 & 2) react together: $\ce{H + H -> H2}$

However, my problem arises when I compare this to my rate law that I found experimentally ($\ce{Mg}$ is not in the rate law as it is a solid and has no concentration):

$$\mathrm{rate} = k[\ce{H+}]^2$$

None of these mechanism steps above conform to my observed rate law (or do they?), could any of you enlighten me to any other mechanisms?

There are only two mechanisms I can think of: a one-step mechanism where it is literally $\ce{Mg + 2H+ -> Mg^2+ + H2}$ (though I've read that a one-step reaction is unlikely) and the other way is via an intermediate (as described above).

Answer 1

Based on the three step mechanism you have provided, what if the slow step is your step 3 which is H + H --> H2 so rate law is now k3[H]^2. Since H is an intermediate, you can substitute for this intermediate from earlier steps and you will end up with Rate = (k3.k1.k2.[Mg][H+]^2)/[Mg2+] and if [Mg]/[Mg2+] is constant as the reaction of a solid always happens at the surface, you can get a rate law = k [HCl]^2

Answer 2

The chemistry of magnesium is somewhat more complicated than you might think. First, $Mg$ metal is always covered with $OH$ groups - $Mg(OH)_2$ is quite insoluble, and so a piece of magnesium does not react with water (pH = 7). Well, not very rapidly, anyway - we say that the magnesium is passivated and corrosion is stifled by its insoluble hydroxide coating.

Magnesium anodes are used in glass-coated steel hot water heaters to delay corrosion of the steel if the glass cracks, exposing the outer casing. Sometimes the magnesium is alloyed with aluminum to change the corrosion chemistry of the anode. So, while magnesium doesn't react with water rapidly, it can be anodic enough to protect steel, especially if it is warmer than room temperature ($Mg(OH)_2$ is more soluble in hot water than in cold).

So, the first step in the reaction of magnesium with water must be the dissolution of some $Mg(OH)_2$. This is also the case with making Grignard reagents: magnesium ribbon hardly ever reacts immediately when you try to make a Grignard. You crack the ribbon under the solvent, you grind away at it, then finally, it just takes off and reacts rapidly. Sometimes you have to add a more reactive organic halide, or iodine. But the idea is to break thru the passive coating to expose bare metal, which is quite reactive.

Magnesium powder can be pyrophoric in air. Once you get it burning, it is difficult to put it out - water won't do it. $CO_2$ won't do it. Dry sand might.

Experimentally, you may determine a rate and develop some formula to describe the rate, but establishing the mechanism will have to take into account the passive layer and how it dissolves. In fact, that may be the only thing you can examine, because when you break thru the passive layer to bare magnesium metal, the reaction rate should zoom up and then be limited by diffusion, stirring, removal of $H_2$ gas bubbles, and who knows what else.