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?

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%

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 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%.