Question

Consider a mixture of potassium chloride and potassium nitrate that is \(43.2 \%\) potassium by mass. What is the percent \(\mathrm{KCl}\) by mass of the original mixture?

Short answer

The mass percentage of KCl in the original mixture is approximately 31.51%.

Step-by-step solution

Calculate the mass percentages of potassium in KCl and KNO₃

First, we need to find the mass percentage of potassium in potassium chloride (KCl) and potassium nitrate (KNO₃) individually. For KCl: - Molar mass of potassium (K) = 39.1 g/mol - Molar mass of chlorine (Cl) = 35.5 g/mol - Molar mass of KCl = 39.1 + 35.5 = 74.6 g/mol - Mass percentage of potassium in KCl = (mass of K / molar mass of KCl) * 100 - Mass percentage of potassium in KCl = (39.1 / 74.6) * 100 ≈ 52.4% For KNO₃: - Molar mass of nitrogen (N) = 14.0 g/mol - Molar mass of oxygen (O) = 16.0 g/mol - Molar mass of KNO₃ = 39.1 + 14.0 + 3 * 16.0 = 101.1 g/mol - Mass percentage of potassium in KNO₃ = (mass of K / molar mass of KNO₃) * 100 - Mass percentage of potassium in KNO₃ = (39.1 / 101.1) * 100 ≈ 38.7%

Set up a linear equation

Let x be the mass percentage of KCl in the mixture and (1 - x) be the mass percentage of KNO₃. According to the given information, 43.2% of the mixture is potassium by mass. We can express this as a linear equation: 43.2 = x (mass percentage of K in KCl) + (1 - x) (mass percentage of K in KNO₃) Substitute the values found in step 1: 43.2 = x (52.4) + (1 - x) (38.7)

Solve the linear equation

Solve the above equation to find the value of x: 43.2 = 52.4x + 38.7 - 38.7x Combine the x terms: 43.2 = 13.7x Now, divide both sides by 13.7: x ≈ 3.15/1 ≈ 0.3151 Convert this value to a percentage: x ≈ 31.51% So, the mass percentage of KCl in the original mixture is approximately 31.51%.

Key concepts

Molar Mass Calculation

Understanding the molar mass of compounds is crucial for determining their chemical properties. Molar mass refers to the mass of one mole of a substance (in grams). It's like a handy tool for chemists to weigh out specific amounts for reactions.

To calculate it, simply add up the atomic masses of all the elements in a compound. These atomic masses can be found on the periodic table. Each element in a compound contributes to its overall molar mass. For instance, hydrogen has an atomic mass of about 1 g/mol, while oxygen's is approximately 16 g/mol.

• The molar mass of water (H₂O) is calculated by adding the masses of two hydrogen atoms and one oxygen atom: \(2(1) + 16 = 18\) g/mol.
• For potassium chloride (KCl), we use the atomic masses of potassium and chlorine: \(39.1 + 35.5 = 74.6\) g/mol.
• In potassium nitrate (KNO₃), add the masses of potassium, nitrogen, and three oxygen atoms: \(39.1 + 14.0 + 3(16.0) = 101.1\) g/mol.

By knowing these values, you can understand how much of each element is present in a compound. It also helps in determining the percentages of each element relative to the whole compound.

Potassium Chloride

Potassium chloride, abbreviated as KCl, is a chemical compound consisting of potassium and chlorine. It's widely known for its role as a common salt substitute due to its potassium content.

The molar mass of potassium chloride is calculated as 74.6 g/mol. This value comes from summing the atomic masses of potassium (39.1 g/mol) and chlorine (35.5 g/mol).

• Potassium, denoted by K, belongs to the alkali metal group on the periodic table.
• Chlorine, Cl, is a halogen, known for its reactivity and presence in many compounds.

In potassium chloride, potassium makes up approximately 52.4% of the compound by mass. This percentage highlights the relatively high content of potassium. KCl serves various purposes, beyond just seasoning food. It's used in medicine, as a fertilizer in agriculture, and even in certain industrial processes.

Understanding its chemical make-up and molar mass helps in applications where precise measurements of potassium are needed. It's important for students to know how to calculate and interpret this, especially in problems dealing with mixtures or solutions.

Potassium Nitrate

Potassium nitrate, known as KNO₃, is a crystalline compound made from potassium, nitrogen, and oxygen. This compound is famous for its use in fertilizer production and in the food industry as a preservative.

The molar mass for potassium nitrate is 101.1 g/mol. It's calculated by adding the atomic masses of its constituent elements: potassium (39.1 g/mol), nitrogen (14.0 g/mol), and three oxygen atoms (16.0 g/mol each).

• Potassium (K) contributes significantly to the total mass, but less so than in KCl due to the presence of nitrogen and oxygen.
• Nitrogen and oxygen add unique properties to KNO₃, making it useful for various explosive applications as well.

The mass percentage of potassium in potassium nitrate is about 38.7%. This signifies the portion of the compound's mass that comes from potassium. When dealing with mixtures, like the exercise problem, knowing this percentage is vital to determining each component's contribution. KNO₃'s unique composition affects how it interacts in chemical processes, especially those requiring a knowledge of potassium's role.

A clear understanding of KNO₃'s molar mass and composition is essential for students to solve problems related to mass percentages in mixtures or solutions.