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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 H_{2}O_{2} – that’s where
you’re going to find the reaction rate.

Your table should have columns for starting concentration of
H_{2}O_{2} (food for thought: how do you really know the
concentration? H_{2}O_{2} 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 O_{2} evolved.

What you need to do with the data in your table is calculate (estimate is
probably a better word) the initial rates of O_{2} evolution for
each initial H_{2}O_{2} 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 O_{2} 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
O_{2} has been produced. On your table, in the initial rate column,
you would enter the volume of O_{2} produced per unit time. The
units would be in ml of O_{2} per minute or per second.

You can then convert from volume of O_{2} to moles of O_{2}
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
O_{2} 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 O_{2}
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

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