# How to write a rate expression when one reactant is not soluble?

For a chemistry experiment, I would like to determine the rate expression for the reaction between zinc and hydrochloric acid. Given that zinc is not soluble in the water, would I use a "false" concentration of sorts and divide the moles of zinc added by the volume of the hydrochloric acid, or is one simply not able to write a rate expression for this reaction?

• Consider if the rate is meaningful: you can determine the degree of the equation, but the actual rate would be dependent on external factors, e.g., Is the zinc a single sphere, a nanometer thick sheet, etc.? What removes hydrogen bubbles that quickly remove Zn from contact with HCl? Gravity? Stirring? Mar 6 at 15:45
• Trying to evaluate reaction rates where three different phases are involved (solid, liquid, gas) is like opening the Pandora's box. Mar 7 at 15:59

(1) About the "false" concentration Hello. In general, a rate law may (among other magnitudes) include some measure of the concentration of all the participants, in this case $$\ce{Zn(s)} + \ce{2 HCl(aq)} \rightarrow \ce{ZnCl_2 (aq)} + \ce{H_2 (g)} \tag{1}$$

As you said correctly, zinc is not soluble on this medium. However, there is no such thing of "concentration of Zinc" or "concentration of a solid", because this is a pure solid, and there is no sense of talking about a measure of concentration of a pure solid phase. Mathematically this is an advantage for you, because the activity of a pure solid phase, is by definition 1, i.e. $$a_{\ce{Zn}} = 1$$ always.

(2) About the possibility to write down a rate law You can, sometimes easily sometimes not, track the concentration of a certain species in this solution. Here may come your knowledge in analytic chemistry for ions in solution for example.

If you can guarantee that only Eq. (1) takes place, this will be enough, and by stoichiometry you can find the moles of all the other species consumed/generated within time. After that, you can perform a mole balance and try to relate the rate of change of any concentration to the rate of reaction. However, finding a general equation that relates the set of experimental values to a rate law $$r$$ that depends on to the concentration of $$\ce{H^+}$$, of $$\ce{Cl^-}$$, the partial pressure of $$\ce{H_2}$$, the temperature $$T$$, etc., is a matter of art. Good luck in your experiment!

In principle, the rate law should include anything that changes the rate, or specify that parameters that were kept constant (temperature, for example). So you could say you investigated the rate law a room temperature and ambient pressure.

[OP] Given that zinc is not soluble in the water, would I use a "false" concentration of sorts and divide the moles of zinc added by the volume of the hydrochloric acid, or is one simply not able to write a rate expression for this reaction?

You would have to do some experiments to see what about the zinc affects the rate. Surface area would be a first guess. It is unlikely that the quantity you suggest would be directly linked to the speed of reaction. I don't think the reaction slows down when you add more hydrochloric acid to a block of zinc (but your "false" concentration would be lower).

[from the comments] What removes hydrogen bubbles that quickly remove Zn from contact with HCl? Gravity? Stirring?

If you stir, you would have to do an experiment whether the type of stirring and the speed of stirring affects the rate (or keep it constant and specify it when you state the rate law and constants, see above).

For a chemistry experiment, I would like to determine the rate expression for the reaction between zinc and hydrochloric acid.

The first rate laws you learn about are often zero, first or second order in a reactant. When it comes to heterogeneous reactions, you can expect more complicated behavior (which might look like zero or first order in same part of the multi-dimensional parameter space). A classic example is enzyme kinetics, where the reaction looks first order in substrate at lower concentration and zero order at higher concentration, with a rate law that is not a simple power law.