Re: rate of reaction equation for hydrogen peroxide and catalase.

Hi Amirah,

Sounds like a great experiment I wish I did in high school. I have good news for you: the rate of reaction is right under your nose. All those measurements you’ve been taking on how much oxygen is being produced for each different concentration of H₂O₂ – that’s where you’re going to find the reaction rate.

Your table should have columns for starting concentration of H₂O₂ (food for thought: how do you really know the concentration? H₂O₂ is unstable and can decompose by itself so do you have an independent measurement of concentration besides measuring a volume from a bottle?), time, catalase concentration, and volume of O₂ evolved.

What you need to do with the data in your table is calculate (estimate is probably a better word) the initial rates of O₂ evolution for each initial H₂O₂ concentration. In some systems, it is very difficult to measure these initial rates because the reactions are so fast that the rate of mixing of the ingredients introduces a lot of error. I’m assuming that in this case, the rate of O₂ evolution is slow enough that you can obtain an accurate estimate of the initial rates (maybe a time scale of 1 or 5 minutes is sufficient).

Let’s assume that within the first minute, a measurable amount of O₂ has been produced. On your table, in the initial rate column, you would enter the volume of O₂ produced per unit time. The units would be in ml of O₂ per minute or per second.

You can then convert from volume of O₂ to moles of O₂ using the ideal gas law (PV = nRT) which I assume you’ve covered before. Then you can have another column for initial rate in units of moles of O₂ per unit time. In this experiment, even though reaction rate appears on the left side of the equation, you are not going to use the equation to calculate reaction rates. Rather, you are going to input reaction rates that come directly from your measurements of O₂ evolution over time, and you are going to be calculating V_max and K_M.

Now that you have all your data, both “raw” (direct measurements) and processed (the calculated initial rates), you can perform a regression to obtain the desired parameters, K_M and V_max. Your question shows that you haven’t grasped the inputs and outputs of this experiment: V_max is not an input, it is an output.

The Michaelis-Menten equation you listed is almost correct for this situation. We just have to be more careful about the units.

The equation you want to use is V = V_max*[S]/(K_M + [S])

Where V represents the reaction velocity (another word for the initial rate) in units of moles of product per unit time. This V is not to be confused with the V in the ideal gas equation I wrote above; there it represents the volume of gas.

The equation you listed in your question had a problem with units, because generally, V_max is expressed in units of moles of product per unit time. It is optional to decompose V_max as V_max = k_cat * E_o, so in the equation you listed in your question, you would need to replace V_max with k_cat. Since E_o, the initial (or total) concentration of enzyme is in units of moles, and since V_max is in units of moles/time, k_cat is in units of inverse-time (like sec^-1). I would just use the equation I listed above. Later, when you have an estimate for V_max, you can calculate k_cat by dividing by E_o.

I mentioned something above that might be confusing you even more than you already are: regression. Essentially, you need to take the proper data from your table and plot it on a graph in a particular way. You will actually need to do more processing of the data to get it in the right form for plotting. I’m including two links for common ways to plot your data in order to extract the parameters V_max and K_M. Both have their flaws, but the Eadie-Hofstee method is probably the more accurate of the two. Even better is to use nonlinear regression, but that is a technique beyond high school and even most undergraduate studies. Note that unless your experiment covered a sufficiently wide margin of different concentrations of substrate, your data may not make it possible to obtain decent estimates of V_max and K_M. Ideally, you want to have data at high enough substrate concentration such that you achieve V_max in your experiment. This is the maximum possible rate of reaction under the given conditions, which cannot be increased any further by adding extra substrate. K_M, the Michaelis constant, also has a physical meaning. It represents the concentration of substrate that yields a rate (V) that is exactly one-half of V_max. In nature, values of K_M range over more than six orders of magnitude.

Here are the links to the regression methods:

http://en.wikipedia.org/wiki/Lineweaver-Burk_plot

http://en.wikipedia.org/wiki/Eadie-Hofstee_plot

-Alex Tobias