4. A chemist carries out an experiment to determine the number of moles of \( \mathrm{Cl}^{-} \)ions in a 1 L sample of water. The salt water reacts with excess \( \mathrm{AgNO}_{3} \) solution. The resulting precipitate is collected, dried and weighed. The mass of the AgCl precipitate is found to be 5.4 g . The chemical equation for the reaction is: \[ \mathrm{AgNO}_{3}(a q)+\mathrm{NaCl}(a q) \rightarrow \mathrm{AgCl}(s)+\mathrm{NaNO}_{3}(a q) \] Calculate the moles of \( \mathrm{Cl}^{-} \)ions in the sample, and describe how the number of moles was found. Re to the periodic table.

To find the moles of \( \mathrm{Cl}^{-} \) ions in the sample, we first need to determine the number of moles of the precipitate \( \mathrm{AgCl} \). The molar mass of \( \mathrm{AgCl} \) is approximately 143.32 g/mol (with silver \( \mathrm{Ag} \) being about 107.87 g/mol and chlorine \( \mathrm{Cl} \) being about 35.45 g/mol). Using the mass of \( \mathrm{AgCl} \) precipitate, we calculate the moles: \[ \text{Moles of } \mathrm{AgCl} = \frac{\text{mass}}{\text{molar mass}} = \frac{5.4 \, \text{g}}{143.32 \, \text{g/mol}} \approx 0.0376 \, \text{mol} \] Because the reaction shows a 1:1 stoichiometry between \( \mathrm{Cl}^- \) and \( \mathrm{AgCl} \), the moles of \( \mathrm{Cl}^- \) ions in the sample are also approximately 0.0376 mol. Understanding the stoichiometry of reactions is crucial, as it helps chemists quantify reactants and products. For instance, in this case, each mole of \( \mathrm{Cl}^- \) generates one mole of precipitate \( \mathrm{AgCl} \). This fundamental principle underlies many laboratory analyses in chemistry and ensures accurate interpretations of experimental results. Using precise measurements and calculations is key in lab work. A common mistake is improperly converting grams to moles due to incorrect molar masses or unit confusion. Always double-check calculations, especially when measuring sample weights or balancing equations. This ensures the integrity of your results, which is especially important when determining concentrations or moles in a solution.