Question

The mass percent of \(\mathrm{Cl}^{-}\) in a seawater sample is determined by titrating \(25.00 \mathrm{~mL}\) of seawater with \(\mathrm{AgNO}_{3}\) solution, causing a precipitation reaction. An indicator is used to detect the end point, which occurs when free \(\mathrm{Ag}^{+}\) ion is present in solution after all the \(\mathrm{Cl}^{-}\) has reacted. If \(53.63 \mathrm{~mL}\) of \(0.2970 \mathrm{M} \mathrm{AgNO}_{3}\) is required to reach the end point, what is the mass percent of \(\mathrm{Cl}^{-}\) in the seawater \((d\) of seawater \(=1.024 \mathrm{~g} / \mathrm{mL}) ?\)

Short answer

The mass percent of \( \text{Cl}^- \) in the seawater is 2.21\text{\text{%}}.

Step-by-step solution

- Determine moles of \( \text{AgNO}_3 \)

Use the molarity and volume of \( \text{AgNO}_3 \) to calculate the moles. \[ \text{Moles of } \text{AgNO}_3 = \text{Molarity} \times \text{Volume} = 0.2970 \text{ M} \times 53.63 \text{ mL} \times \frac{1 \text{L}}{1000 \text{ mL}} = 0.01592211 \text{ mol} \]

- Use stoichiometry to find moles of \( \text{Cl}^- \)

From the balanced reaction, \( \text{AgNO}_3 + \text{Cl}^- \rightarrow \text{AgCl} \), the molar ratio is 1:1. Therefore, \[ \text{Moles of } \text{Cl}^- = \text{Moles of } \text{AgNO}_3 = 0.01592211 \text{ mol} \]

- Calculate the mass of \( \text{Cl}^- \)

Use the moles of \( \text{Cl}^- \) and the molar mass of chlorine (35.45 g/mol) to find the mass. \[ \text{Mass of } \text{Cl}^- = 0.01592211 \text{ mol} \times 35.45 \text{ g/mol} = 0.5649 \text{ g} \]

- Determine the mass of seawater sample

Find the mass of the seawater using its density and volume. \[ \text{Mass of seawater} = 25.00 \text{ mL} \times 1.024 \text{ g/mL} = 25.60 \text{ g} \]

- Calculate the mass percent of \( \text{Cl}^- \) in seawater

The mass percent can be found using the formula: \[ \text{Mass percent of } \text{Cl}^- = \frac{\text{Mass of } \text{Cl}^-}{\text{Mass of seawater}} \times 100 = \frac{0.5649 \text{ g}}{25.60 \text{ g}} \times 100 = 2.21\text{\text{%}} \]

Key concepts

titration

Titration is an analytical technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration. In this exercise, we titrate seawater with a solution of \( \text{AgNO}_3 \), which reacts with \( \text{Cl}^- \) ions present in the seawater. The point at which all the \( \text{Cl}^- \) ions have reacted is known as the endpoint. We use an indicator to detect this endpoint, which changes color when free \( \text{Ag}^+ \) ions are present, signaling that the titration is complete.

molarity

Molarity (\(M\)) is a way to express the concentration of a solution. It is defined as the number of moles of a solute per liter of solution. In this problem, the molarity of \( \text{AgNO}_3 \) is given as 0.2970 M. To find the moles of \( \text{AgNO}_3 \) used in the titration, we use the formula: \[ \text{Moles of AgNO}_3 = \text{Molarity} \times \text{Volume} \]

stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of reactants and products. In our exercise, the reaction between \( \text{AgNO}_3 \) and \( \text{Cl}^- \) can be represented as: \[ \text{AgNO}_3 + \text{Cl}^- \rightarrow \text{AgCl} \] The molar ratio is 1:1, meaning one mole of \( \text{AgNO}_3 \) reacts with one mole of \( \text{Cl}^- \). This stoichiometric relationship is used to convert the moles of \( \text{AgNO}_3 \) to moles of \( \text{Cl}^- \).

precipitation reaction

A precipitation reaction occurs when two soluble substances react to form an insoluble product, known as a precipitate. In this case, \( \text{AgNO}_3 \) reacts with \( \text{Cl}^- \) ions in seawater to form \( \text{AgCl} \), which is insoluble in water. The reaction is: \[ \text{AgNO}_3 + \text{Cl}^- \rightarrow \text{AgCl} \] The formation of the solid \( \text{AgCl} \) precipitate is the key to determining the amount of \( \text{Cl}^- \) in the sample through the titration process.

mass percent calculation

Mass percent is a way to express the concentration of a component in a mixture. It is calculated using the formula: \[ \text{Mass percent} = \frac{\text{Mass of component}}{\text{Total mass of mixture}} \times 100 \] In our exercise, to find the mass percent of \( \text{Cl}^- \) in seawater, we first determine the mass of \( \text{Cl}^- \) from the moles calculated through titration. Then, we find the mass of the seawater sample using its volume and density. Finally, we use the formula to calculate the mass percent of \( \text{Cl}^- \) in the seawater, which gives us the concentration of chloride ions.