Amount of substance q help

Can someone explain how to do this question please? I don’t understand any of the mark scheme

This is called a back titration.

You start with an excess of HCl and react it with a small amount of your analyte (in this case, Na2CO3.xH2O). You then use a titration to work out how much of the HCl is left, so that you can work out how many moles of HCl it took to react with the analyte and therefore how many moles of the analyte were present.

M1 is simply using the equation moles = concentration in mol dm^-3 x volume in dm^3. They’ve told you that [HCl] initially is 0.25 mol dm^-3 and the volume of HCl is 200 cm^3 (or 0.2 dm^3) and also that [NaOH] is 0.15 dm^3 and that it takes 26.60 cm^3 (0.0266 dm^3) to react with what is left of the HCl in the 25 cm^3 of diluted solution. You have all the numbers you need to get the moles given in the MS.

M2 is a little more tricky to understand. After reacting the HCl with sodium carbonate, they diluted the solution to 250 cm^3 and took only 25 cm^3 of it. That means that the total moles of HCl determined to be in the 25 cm^3 is only one tenth of what is left after the reaction. Because NaOH and HCl react in a 1:1 ratio, the moles of HCl left in the 25 cm^3 = the moles of NaOH in the titre. Therefore, the moles of HCl left in the 250 cm^3 of solution is 10 x the moles of NaOH in the titre.

M3 is using original moles of HCl - final moles of HCl = change in moles of HCl as a result of the first reaction (i.e the reaction of HCl with the Na2CO3.xH2O).

M4 is using the fact that 1 mole of Na2CO3.xH2O reacts with 2 moles of HCl, so the moles of Na2CO3.xH2O = 1/2 x change in moles of HCl.

M5 is dividing 627 mg by 1000 to convert it to grams.

M6 is using the fact that mass in grams = moles x molar mass. As such, the molar mass of Na2CO3.xH2O is given by (0.627 g)/(5.05 x 10^-3 moles) ≈ 124. Using the periodic table, the Mr of Na2CO3 is 106 and the Mr of H2O is 18. The molar mass of Na2CO3.xH2O is therefore 106 + 18x, because it is made up of one unit of Na2CO3 and x units of water. So therefore 124 = 106 + 18x ==> 18 = 18x

M7 is therefore deducing that x = 1

Thank you for the help. I understand it all apart from the fact that hcl reacts with na2co3xh2o in a 2 to 1 ratio. How do you figure that out? Would you just write an equation, if so what would it be? Thanks.