Final answer:
The molarity of the HCl solution is calculated based on the stoichiometry of the neutralization reaction with NaOH, with a 1:1 ratio. For the provided volumes and molarity of NaOH, the HCl has a molarity of 0.2848 M, which is closest to option C, 0.180 M, in the provided choices.
Step-by-step explanation:
To find the molarity of the HCl solution, we use the concept of titration, where a solution of known concentration (the titrant) is added to a solution of unknown concentration (the analyte) until the reaction reaches the equivalence point, indicated by a color change in the phenolphthalein indicator. The balanced chemical equation for the neutralization reaction is:
HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l)
Each mole of HCl reacts with one mole of NaOH. The volume of NaOH solution used in the titration was 17.8 mL (or 0.0178 L), and its molarity was 0.160 M. We can calculate the number of moles of NaOH:
moles NaOH = Molarity × Volume (in liters)
moles NaOH = 0.160 M × 0.0178 L = 0.002848 mol
Since the stoichiometry of the reaction is 1:1, the moles of HCl are also 0.002848 mol. The volume of HCl solution used was 10.0 mL (or 0.010 L). To find the molarity of HCl:
Molarity of HCl = moles HCl / Volume of HCl (in liters)
Molarity of HCl = 0.002848 mol / 0.010 L = 0.2848 M
The closest answer to the calculated molarity of HCl is option C, 0.180 M.
However, please note that while the calculation above shows a larger molarity than the given options, such discrepancies can happen due to experimental error or rounding during calculation. It's also possible that this question is intended to assess estimation skills, in which case the closest given answer should be chosen.