What would the pH of a .0037 Molar solution of sulfuric acid be and
how would I go about figuring it out?

Hello s5237-ga,

Thank-you for your question.

To answer the question we need to know what pH is and how it relates
to concentration (or molarity).

There are excellent summaries in the Wikipedia:
http://en.wikipedia.org/wiki/Molarity
http://en.wikipedia.org/wiki/PH

"pH is a measure of the activity of hydrogen ions (H+) in a solution
and, therefore, its acidity or alkalinity. For dilute solutions,
however, it is convenient to substitute the activity of the hydrogen
ions with the molarity (mol/L) of the hydrogen ions (however, this is
not necessarily accurate at higher concentrations)."
http://en.wikipedia.org/wiki/PH

The equation we need to know to solve our problem is:

pH = -log[H+]

where [H+] is the concentration of Hydrogen ions in the solution (in
our question, as we have a dilute solution we can assume [H+] to be
equivalent to the molarity of the solution).

If we then plug the numbers into the equation we get:

pH = -log[H+]
pH = -log(0.0037)
pH = 2.43 (2 decimal places)

This answer can be verified using the online pH Calculator here:
http://www.sensorex.com/support/education/pH_calculator.html

There are also some nicely written classroom style notes here:
http://cstl-csm.semo.edu/rodgers/CH180f2fF03/Dec09tutorial.htm

If you require any further assistance on this subject please do not
hesitate to ask and I will try to answer as soon as possible.

Thank you very much for your help. I was making it more difficult than
it had to be!!

I don't know if this is for a class or for another purpose, but you
should note that sulfuric acid has two hydrogens that can dissociate,
and this can complicate matters.

The first dissociation is strong (i.e., complete), but the second
dissociation is "weaker" and the second hydrogen will not dissociate
completely except at fairly low concentrations.

palitoy-ga lists these notes:

http://cstl-csm.semo.edu/rodgers/CH180f2fF03/Dec09tutorial.htm

which show that sulfuric acid produces two H+ if it dissociates
completely. The concentration used in those notes is 100 times less
than the 0.0037 M you are using, and the author of the notes assumes
complete dissociation of both hydrogens at the concentration he is
using.

If both hydrogens also dissociate completely in the 0.0037 M sulfuric
acid, the H+ concentration would be .0074 M and the pH would be 2.13.

If you are expected to use dissociation constants and account for the
partial dissociation of the second hydrogen, you will have to solve a
quadratic equation. (If this is for a class, you might not be expected
to go that far. In any case, such a more precisely "calculated" pH
would be between 2.43 and 2.13.)

Re: the online calculator and the notes: The online pH calculator
assumes no dissociation of the second hydrogen. If you use it to
calculate the pH of 0.0000296 M sulfuric acid [the concentration used
in the example in the notes], the calculator yields a pH of 4.53,
while the worked out example in the notes site yielded a pH of 4.23.

Thank you for your comments. This is for a class and I am completely
confused. I will post the entire problem and then maybe that will
help:
1) chemo synthetic bacteria are a group of microorganisms known to
survive in extreme conditions of temperature, pressure and pH. A
particular group of these organisms can survive in environments with
pH values as low as 2. A researcher measures the concentration of
sulfuric acid  in a hydrothermal vent and finds it to be 0.0037Molar.
I) Do you expect to find any of these particular organisms existing in
these conditions? Why or why not? II) This same researcher analyzes an
"acid mine drain"  and was surprised to find the area teeming with
life since he measured the sulfuric acid concentration in the drain to
be 0.0019Molar. Is this the same group of organisms he found in the
previous vent? Why or why not? III) What is the equivalent weight of
the sulfuric acid? and what is the normality of the solution in both
cases?
Our teacher told us to remember that H2SO4 is a diprotic acid that
will create 2 H+ ions but I am confused how to use that information.
So the answer that I need will take that into consideration. Thanks a
bunch for your help!!

Go with the "sulfuric acid molarity to pH" calculation given in the
example in the notes-type reference listed by palitoy-ga.

1.  I: You will get a pH of 2.13; pH = -log [H+], or - log [2 *
0.0037]. One H2SO4 dissociates to give 2 H+.

The criterion for bacterial survival is that the pH should be 2 or greater.

1. II: Calculate the pH for 0.0019 M sulfuric acid the same way. This
will tell you whether or not the same bacteria could theoretically
survive in the mine water.

With regard to bacteria from the two sites being the same
microorganism, all you will know is whether the bacteria from the two
sites can survive at low pH; however, there are other environmental
differences that may either be necessary for survival or that preclude
survival of the same organism at both sites. You probably have some
idea of what these differences are.

(Your calculation can ignore the fact that the second hydrogen does
not dissociate completely; taking that into account would only mean
that the pH is somewhat greater than calculated above and won't affect
your decision.)