stoichiometric ratio

Question

I have an unknown sample of carbonate. The pressure and volume were measured after the temperature stabilized at 21.5C.  Given the data below what is the stoichiometric ratio between HCl and CO2?

Initial pressure (atm) :1.00 atm

initial gas volume (ml):  240.0mL

volume of 1.00 HCl solution added to fully consume carbonate sample:  22.0 mL

final pressure (atm):  2.32atm

final gas volume (ml):  218.0 mL

I don't know how to set up the equation to figure this out.

Answer 1

CO₃^2- + 2H⁺ ==> CO₂ + H₂O 

The ratio of HCl to CO₂ must be 1:1

It isn't clear how the experiment was conducted, and not sure what the initial gas volume is supposed to be.  If you simply place an unknown carbonate in a vessel, there is no gas, so what does "initial gas volume" of 240 ml mean?

Taking the other data, you can calculate moles from PV = nRT and n = PV/RT = (2.32 atm)(0.218 L)/(0.082 Latm/Kmol)(294.5K) = 0.021 moles CO₂ gas.

Calculating moles of HC, you have 0.022 L x 1 mol/L = 0.022 moles HCl.  Again, this is a ratio of 1:1 with CO₂.