To determine the concentration of the hydrochloric acid solution, we can use the concept of stoichiometry and the volume of the standard solution (sodium carbonate) that reacts with the hydrochloric acid.
First, let's set up the balanced chemical equation for the reaction between hydrochloric acid (HCl) and sodium carbonate (Na2CO3):
2HCl + Na2CO3 -> 2NaCl + H2O + CO2
From the equation, we can see that two moles of hydrochloric acid react with one mole of sodium carbonate.
Given that 27.8 cm^3 of hydrochloric acid were used to neutralize 25 cm^3 of the sodium carbonate, we can use the volume ratio to determine the moles of hydrochloric acid involved in the reaction.
Volume(HCl) / Volume(Na2CO3) = Moles(HCl) / Moles(Na2CO3)
27.8 cm^3 / 25 cm^3 = Moles(HCl) / 1 mole
Moles(HCl) = 27.8 cm^3 / 25 cm^3
Now, since two moles of hydrochloric acid react with one mole of sodium carbonate, we can say:
Moles(HCl) = 2 * Moles(Na2CO3)
Substituting the value of Moles(HCl) into the equation:
27.8 cm^3 / 25 cm^3 = 2 * Moles(Na2CO3) / 1 mole
Moles(Na2CO3) = (27.8 cm^3 / 25 cm^3) / 2
Now, we can calculate the concentration of the hydrochloric acid solution.
Concentration(HCl) = Moles(HCl) / Volume(HCl)
Assuming the volume of hydrochloric acid used is also 27.8 cm^3:
Concentration(HCl) = (27.8 cm^3 / 25 cm^3) / 27.8 cm^3
Concentration(HCl) = (27.8 cm^3 / 25 cm^3) * (1 / 27.8 cm^3)
Concentration(HCl) = 1 / 25
Concentration(HCl) = 0.04 M
Therefore, the concentration of the hydrochloric acid solution is 0.04 M.