Question

Use Dalton's theory to explain why potassium nitrate from India or Italy has the same mass percents of \(\mathrm{K}, \mathrm{N},\) and \(\mathrm{O}\).

Short answer

Due to Dalton's theory, potassium nitrate has identical mass percentages of K, N, and O regardless of origin because it always has the same molecular structure.

Step-by-step solution

- Understand Dalton's Atomic Theory

Dalton's Atomic Theory states that elements are made of tiny, indivisible particles called atoms, and atoms of the same element are identical in mass and properties. Compounds are formed by the combination of different types of atoms in specific ratios.

- Define Potassium Nitrate

Potassium nitrate (KNO₃) is a chemical compound consisting of potassium (K), nitrogen (N), and oxygen (O) atoms. Its molecular formula indicates it is composed of 1 potassium atom, 1 nitrogen atom, and 3 oxygen atoms.

- Discuss the Consistency of Atoms

According to Dalton's theory, the potassium atoms in a sample of potassium nitrate from India are identical to the potassium atoms in a sample of potassium nitrate from Italy. The same applies to the nitrogen and oxygen atoms.

- Explain Mass Percent Consistency

Because potassium nitrate has a consistent molecular formula (KNO₃), the ratio of potassium, nitrogen, and oxygen atoms is fixed. The mass percent of each element in potassium nitrate remains constant regardless of the sample's geographic origin.

- Calculate Mass Percentages

To verify, calculate the mass percentages: The molecular masses are approximately K = 39.1, N = 14.0, O = 16.0. The molar mass of KNO₃ = 39.1 + 14.0 + (3 * 16.0) = 101.1 g/mol. Calculate mass percent for each element: Potassium: \(\frac{39.1}{101.1} \times 100\%\) ≈ 38.7%. Nitrogen: \(\frac{14.0}{101.1} \times 100\%\) ≈ 13.8%. Oxygen: \(\frac{3 \times 16.0}{101.1} \times 100\%\) ≈ 47.5%.

- Conclusion

Since the molecular structure and atomic composition of potassium nitrate are the same, its mass percents of K, N, and O will be identical regardless of the source, consistent with Dalton's theory.

Key concepts

atomic theory

Dalton's Atomic Theory is a fundamental concept in chemistry that explains the nature of matter. According to this theory, everything is made up of tiny particles called atoms. These atoms are indivisible and cannot be created or destroyed in chemical reactions. One key point of Dalton’s Atomic Theory is that atoms of the same element are identical. This means all potassium atoms, for example, have exactly the same mass and properties, no matter where they are found. Dalton also introduced the idea that chemical compounds form when atoms of different elements combine in definite, fixed ratios. This understanding helps explain why potassium nitrate from India and Italy would have the same composition and properties.

chemical compounds

A chemical compound is a substance formed when two or more different kinds of atoms bond together. Potassium nitrate (KNO₃) is an example of a chemical compound. It consists of potassium (K), nitrogen (N), and oxygen (O) atoms. The molecular formula KNO₃ tells us that in each molecule of potassium nitrate, there is 1 atom of potassium, 1 atom of nitrogen, and 3 atoms of oxygen. Chemical compounds have fixed compositions. This means no matter where the compound is from, its composition remains the same. In our example, every molecule of potassium nitrate will always be made up of exactly 1 potassium atom, 1 nitrogen atom, and 3 oxygen atoms, whether the potassium nitrate is sourced from India or Italy.

mass percentage

Mass percentage is a way of expressing the concentration of an element in a compound. It is calculated by dividing the mass of the element by the total mass of the compound and then multiplying the result by 100%. Let's look at potassium nitrate (KNO₃) as an example. The molar mass of KNO₃ is calculated by adding the atomic masses of potassium (39.1 g/mol), nitrogen (14.0 g/mol), and oxygen (3 * 16.0 g/mol), which equals 101.1 g/mol. To find the mass percent of potassium, you divide 39.1 by 101.1 and multiply by 100%, giving approximately 38.7%. Similarly, the mass percentage of nitrogen is calculated as (14.0 / 101.1) * 100% ≈ 13.8%, and for oxygen, it is (3 * 16.0 / 101.1) * 100% ≈ 47.5%. These percentages will be the same for any sample of potassium nitrate, no matter where it originates, because the molecular formula KNO₃ is consistent.