Question

The mass percentage of chloride ion in a \(25.00\)-mL sample of seawater was determined by titrating the sample with silver nitrate, precipitating silver chloride. It took \(42.58 \mathrm{~mL}\) of \(0.2997 \mathrm{M}\) silver nitrate solution to reach the equivalence point in the titration. What is the mass percentage of chloride ion in seawater if its density is \(1.025 \mathrm{~g} / \mathrm{mL}\) ?

Short answer

The mass percentage of chloride ion in seawater can be calculated in 4 steps: 1. Calculate moles of chloride ions: Moles of Cl- = \(42.58 \mathrm{~mL}\) × \(0.2997 \mathrm{M}\). 2. Calculate mass of chloride ions: Mass of Cl- = Moles of Cl- × \(35.45 \mathrm{~g/mol}\). 3. Calculate mass of seawater sample: Mass of seawater = \(1.025 \mathrm{~g/mL}\) × \(25.00 \mathrm{~mL}\). 4. Calculate mass percentage of chloride ion: Mass percentage of Cl- = \((\text{Mass of Cl-} / \text{Mass of seawater}) × 100\). Substitute the values from steps 1-3 into step 4 formula to find the mass percentage of chloride ion in seawater.

Step-by-step solution

Calculate moles of chloride ions

To calculate the moles of chloride ions, we'll first need to find the moles of AgNO3 used in the titration. Moles of AgNO3 = Volume of AgNO3 × Concentration of AgNO3 Given: Volume of AgNO3 = 42.58 mL and Concentration of AgNO3 = 0.2997 M Molar Ratio = 1 AgNO3 mole : 1 Cl- mole Since 1 mole of AgNO3 reacts with 1 mole of Cl-, the moles of Cl- ions will be equal to the moles of AgNO3.

Calculate mass of chloride ions

Now, we can find the mass of chloride ions by using the formula: Mass of Cl- = Moles of Cl- × Molar mass of Cl- The molar mass of Cl- is approximately 35.45 g/mol.

Calculate mass of seawater sample

To calculate the mass percentage of chloride ion in seawater, we need to find the mass of the seawater sample. Density of seawater = 1.025 g/mL Mass of seawater = Density × Volume of seawater Given: Volume of seawater = 25.00 mL

Calculate mass percentage of chloride ion in seawater

Now, we can calculate the mass percentage of chloride ion using the formula: Mass percentage of Cl- = (Mass of Cl- / Mass of seawater) × 100 After finding the mass of Cl- in step 2 and mass of seawater in step 3, substitute the values into the above formula to find the mass percentage.

Key concepts

Titration

Titration is a laboratory method used to determine the concentration of a reactant in a solution. It involves the gradual addition of a titrant, which is a solution of known concentration, to a known volume of a solution with an unknown concentration. The goal is to reach the equivalence point, where the reactants have reacted completely. In the example of titrating seawater with silver nitrate, the titrant (silver nitrate) reacts with the chloride ions in the seawater until all the chloride ions have precipitated as silver chloride. This approach allows for precise quantitative analysis of the chloride ions present in the seawater sample. The volume of titrant used to reach this point helps to calculate the amount of chloride ions in the solution.

Molar Mass Calculations

Molar mass is the mass of one mole of a substance expressed in grams per mole (g/mol). It is used to convert between grams and moles of a substance. In our exercise, we used the molar mass of the chloride ion, which is approximately 35.45 g/mol, to find the mass of chloride ions present in the titrated seawater.

The moles of chloride ions were calculated first by using the known moles of silver nitrate, due to the 1:1 stoichiometric reaction ratio. Then, using the molar mass formula, Mass = Moles × Molar Mass, we determined the mass of chloride ions. This conversion is critical for understanding the proportion of chloride ions present in our seawater sample.

Density Calculations

Density is the mass of a substance per unit volume. It is usually expressed in grams per milliliter (g/mL) for liquids. In the seawater composition exercise, we have a given density of 1.025 g/mL. This value is utilized to find the mass of the seawater sample.

Using the formula Mass = Density × Volume, and with the seawater volume being 25.00 mL, we can calculate the mass of the seawater. This calculation is important as it helps establish a relationship between the physical properties of the sample and the results obtained from the titration.

Mass Percentage

The mass percentage is a way to express the concentration of an element or component in a mixture or compound. It is expressed as the mass of the component divided by the total mass of the mixture, multiplied by 100. This makes it a convenient measure especially when dealing with solutions like seawater.

In our analysis, after calculating the mass of chloride ions and the mass of the seawater, these values were substituted into the mass percentage formula: \[\text{Mass percentage of Cl}^- = \left( \frac{\text{Mass of Cl}^-}{\text{Mass of seawater}} \right) \times 100\] This calculation provides a clear understanding of how much of the seawater's mass is constituted by chloride ions.

Seawater Composition

Seawater is a complex solution that contains a variety of dissolved ions, with chloride ions being one of the most significant components. Understanding its composition is essential for numerous applications, including oceanography, marine biology, and environmental science.

The analysis of seawater often requires determining the concentration of individual ions, and titration is a practical technique to achieve this. By knowing the concentration of chloride ions, one can infer important properties and behaviors of seawater under different conditions. Additionally, it aids in understanding the salinity, which affects factors such as density and buoyancy critical for marine life and ocean currents.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react in a solution to form one or more insoluble products, known as precipitates. In the context of seawater chloride ion analysis, the reaction between silver ions (\(Ag^+\)) and chloride ions (\(Cl^-\)) is a classic example.

During titration, silver nitrate (\(AgNO_3\)) is added to seawater, leading to the reaction:\[Ag^+ + Cl^- \rightarrow AgCl(s)\] Here, silver chloride (\(AgCl\)) precipitates out as a solid. This reaction's occurrence is signaled by the cloudy appearance of the solution due to the formation of the white silver chloride precipitate. Such reactions are fundamental in quantitative analysis as they allow for the precise determination of ion concentrations in solutions.