I titrated 0.25g of soda ash mixed with 25mL of deionized water and it took 43.7mL of hydrochloric acid to complete the titration.

I am trying to figure out how to find the moles of sodium carbonate in the soda ash and then the percent of sodium carbonate in the soda ash. How would I go about doing this calculation?

It's important to know what you used as an indicator. If you used phenolphthalein you titrated to the HCO3^- end point. If you used methyl orange or methyl red you titrated to the H2CO3 (H2O + CO2) end point. I will assume that's the one you used.(I think M.R. is better than M.O. but I believe you want to change about pH of 5)

In addition you don't give the molarity of the HCl.

mols HCl = M x L = ?
mols Na2CO3 = 1/2 mols HCl(from the equation of
Na2CO3 + 2HCl ==> 2NaCl + H2O + CO2
g Na2CO3 = mols Na2CO3 x molar mass Na2CO3.
Then %Na2CO3 = (g Na2CO3/0.25g)*100 = ?

I used bromophenol blue as the indicator, and the molarity of HCl is 0.2M.

You titrated to the CO3^2- end point so the equation chemistry is what I indicated. I've never used that indicator. I always used methyl red and titrated until the indicator turned, heated to drive off CO2 (the m.r. turned back basic, and I titrated to the end point (much sharper end point the second time around). Since bromophenolblue turns at a more acid end point, you may not be required to heat the solution to drive off CO2.

I have done the calculation for this multiple times and I keep getting over 100% for the sodium carbonate in soda ash. I have no idea what I am doing wrong. I did it the way that you explained.

To find the moles of sodium carbonate in the soda ash, you need to use the balanced chemical equation for the reaction between sodium carbonate (Na2CO3) and hydrochloric acid (HCl):

Na2CO3 + 2HCl → 2NaCl + H2O + CO2

First, calculate the molarity of the hydrochloric acid solution using the volume of hydrochloric acid used in the titration. In this case, it is 43.7 mL:

Molarity (M) = (moles of solute) / (volume of solution in liters)

Convert the volume used to liters by dividing by 1000:

Volume (L) = 43.7 mL / 1000 = 0.0437 L

Now, calculate the molarity using the balanced equation:

2HCl = 1 mole of Na2CO3

Molarity of HCl = moles of HCl / volume (L) of HCl used

Since the balanced equation shows that 2 moles of HCl react with 1 mole of Na2CO3, the moles of HCl used in the titration would be half of the moles of Na2CO3. Therefore:

Moles of Na2CO3 = (Molarity of HCl) * (Volume of HCl used in L) / 2

Next, calculate the molar mass of sodium carbonate (Na2CO3) which is the sum of the atomic masses of its constituents:

Na: 22.99 g/mol
C: 12.01 g/mol
O: 16.00 g/mol

Molar mass of Na2CO3 = (2 * atomic mass of Na) + atomic mass of C + (3 * atomic mass of O)

Now, calculate the mass of sodium carbonate in the sample using the relationship between moles and mass:

Mass (g) of Na2CO3 = Moles of Na2CO3 * Molar mass of Na2CO3

Finally, calculate the percent of sodium carbonate in the soda ash:

Percent Na2CO3 = (Mass of Na2CO3 / Mass of soda ash) * 100

In this case, the mass of soda ash is given to be 0.25 g. So substitute the calculated values into the equation to find the percent of sodium carbonate in the soda ash.