You are given solutions of HCl and NaOH and must determine their concentrations. You use 38 mL of NaOH to titrate 100 mL of HCl and 23.2 mL of NaOH to titrate 50 mL of 0.0782 M H2SO4. Find the unknown concentrations.

I think you made a typo in the question. You were given unknown solns of HCl and H2SO4?

HCl + NaOH ==> NaCl + H2O
moles NaOH = M x L
moles HCl = same (since equation shows 1:1).
M HCl = moles/L

H2SO4 + 2NaOH ==> Na2SO4 + 2H2O
moles NaOH = M x L
moles H2SO4 = 1/2 moles NaOH (look at the equation).
M H2SO4 = moles/L

To determine the unknown concentrations of HCl and NaOH, we can use the concept of stoichiometry applied to titration. In a titration, a solution of known concentration (the titrant) is added to a solution of unknown concentration until the reaction is complete.

Let's start with the titration of NaOH with HCl. The balanced equation for this reaction is:

NaOH + HCl -> NaCl + H2O

From the given information, we know that it took 38 mL of NaOH to completely react with 100 mL of HCl. To find the concentration of HCl, we can use the equation:

M1V1 = M2V2

Here, M1 represents the concentration of NaOH (which is known and can be assumed to be 1 M), V1 is the volume of NaOH used (38 mL), M2 is the concentration of HCl, and V2 is the volume of HCl (100 mL).

Plugging in the values:

1 M * 38 mL = M2 * 100 mL

M2 = (1 M * 38 mL) / 100 mL
M2 = 0.38 M

So, the concentration of HCl is 0.38 M.

Now let's move on to the second titration, where NaOH is used to titrate H2SO4. The balanced equation for this reaction is:

2 NaOH + H2SO4 -> Na2SO4 + 2 H2O

From the given information, we know that it took 23.2 mL of NaOH to completely react with 50 mL of a 0.0782 M H2SO4 solution. Similarly to the previous calculation, we can use the stoichiometry equation to find the unknown concentration.

1 M * 23.2 mL = (0.0782 M) * 50 mL

Rearranging the formula:

M2 = (0.0782 M * 50 mL) / 23.2 mL
M2 = 0.1699 M

So, the concentration of NaOH is 0.1699 M.

To summarize, after titration, we found that the concentration of HCl is 0.38 M and the concentration of NaOH is 0.1699 M.