Question

The analysis of a sample of soil weighing \(0.4210 \mathrm{~g}\) yields a mixture of \(\mathrm{KCl}\) and \(\mathrm{NaCl}\) weighing \(0.0699 \mathrm{~g} .\) From the \(\mathrm{KCl}\), \(0.060 \mathrm{~g} \mathrm{AgCl}\) is precipitated out. Calculate the percent of \(\mathrm{KC} 1\) in the soil.

Short answer

The percent of KCl in the soil is 7.41%.

Step-by-step solution

Identify the known values

We are given the following: Mass of soil sample: 0.4210 g Mass of KCl and NaCl mixture in the soil sample: 0.0699 g Mass of AgCl precipitated from KCl in the mixture: 0.060 g

Calculate the number of moles of AgCl

To calculate the number of moles of AgCl, we will use its molar mass (143.32 g/mol) and the mass given: Moles of AgCl = mass / molar mass Moles of AgCl = 0.060 g / 143.32 g/mol Moles of AgCl = \(4.18 \times 10^{-4} \mathrm{~mol}\)

Use stoichiometry to determine the number of moles of KCl

Since the reaction between KCl and AgCl is a 1:1 reaction, the number of moles of KCl will be the same as the number of moles of AgCl: Moles of KCl = \(4.18 \times 10^{-4} \mathrm{~mol}\)

Convert moles of KCl to grams

To find the mass of KCl in the mixture, we will multiply the number of moles by the molar mass of KCl (74.55 g/mol): Mass of KCl = moles × molar mass Mass of KCl = \(4.18 \times 10^{-4} \mathrm{~mol} \times 74.55 \mathrm{~g/mol}\) Mass of KCl = 0.0312 g

Calculate the percent of KCl in the soil

To find the percent of KCl in the soil sample, we will divide the mass of KCl by the mass of the soil sample and multiply by 100%: Percentage of KCl in soil = (Mass of KCl / Mass of soil sample) × 100% Percentage of KCl in soil = (0.0312 g / 0.4210 g) × 100% Percentage of KCl in soil = 7.41%

Key concepts

Chemical Analysis

Chemical analysis is a process used to identify the composition of different substances present in a sample. In the context of this exercise, a soil sample is analyzed to determine its potassium chloride (KCl) and sodium chloride (NaCl) content. Here's how chemical analysis works in a simple way:

• A sample is taken and weighed.
• Chemical reactions are performed to separate the components.
• Measurements are made to deduce the amounts of different substances present.

Chemical analysis in this scenario helps find how much of the soil's weight is made up by KCl, which has practical implications for understanding soil properties.

Molar Mass

Molar Mass is the weight of one mole of a given substance and is expressed in grams per mole (g/mol). It allows for easy calculation of the number of moles in a given mass. For example, in this exercise, the molar mass of silver chloride (AgCl) is 143.32 g/mol. This helps convert a weight of AgCl found in the soil into moles. The formula used is: \[\text{Moles} = \frac{\text{Mass of the substance}}{\text{Molar Mass}}\] By knowing the molar mass of KCl (74.55 g/mol), we calculate the mass of KCl present from its moles determined through stoichiometry. Molar mass serves as a bridge between the mass of a substance and the number of particles or moles it contains.

Precipitation Reactions

Precipitation reactions occur when two aqueous solutions mix, and an insoluble solid, known as a precipitate, forms. In the exercise, the reaction between KCl and silver nitrate (AgNO3) forms silver chloride (AgCl), a precipitate. This reaction is described by the chemical equation:\[\text{KCl}_{(aq)} + \text{AgNO}_3{}_{(aq)} → \text{AgCl}_{(s)} + \text{KNO}_3{}_{(aq)}\]These reactions are useful for identifying components because the formation of a precipitate confirms the presence of particular ions. In the exercise, the formation of AgCl guarantees the presence of chloride ions (from KCl) in the soil. This is why precipitation reactions are a central tool in chemical analysis, especially in identifying and quantifying ions in a sample.

Percent Composition

Percent composition refers to the percentage by mass of each element present in a compound. In this exercise, it specifically refers to the percentage of KCl in the soil sample. To calculate the percent composition, divide the mass of KCl by the total mass of the soil sample, and multiply the result by 100%:\[\text{Percent Composition} = \left(\frac{\text{Mass of KCl}}{\text{Mass of soil sample}}\right) \times 100\%\]In the example given, the calculated mass of KCl is used to determine that KCl makes up 7.41% of the soil. Percent composition is a key concept in stoichiometry, providing insights into the proportions of different substances within a mixture, which is essential for applications ranging from material science to pharmacology.