Atomic Foundations of Matter · Lesson 2 of 14
Law of Constant Proportions
“A pure compound keeps the same mass ratio of its elements no matter where the sample came from.”
• State the Law of Constant Proportions. • Explain why purified water from different sources has the same composition. • Use mass ratios to calculate an unknown component. • Distinguish fixed composition of a compound from variable composition of a mixture. • Interpret percentage composition using the cinnabar example.
Two bottles of water may have come from completely different places. One may have begun as river water and another as ocean water. After the samples are purified so that the substance being compared is water itself, their hydrogen and oxygen are found in the same mass relationship. A pure compound has a composition that is characteristic of that compound.
Law of Constant Proportions
In a given compound, the constituent elements are always present in a fixed ratio by mass, irrespective of the source or method of obtaining the compound.
The same idea is also called the Law of Definite Proportions or Proust's Law. Joseph Proust supported it through careful study of the composition of compounds.
Water Has a Fixed Composition
Pure water contains hydrogen and oxygen in the mass ratio 1:8. Therefore, if 9 g of pure water is decomposed completely, the composition corresponds to 1 g of hydrogen and 8 g of oxygen. A different pure-water sample follows the same ratio.
This law concerns a compound, not the impurities or dissolved substances that may accompany it in a natural source. River water and ocean water can contain very different dissolved materials, but once a sample of pure water is considered, the composition of that compound remains definite.
Cinnabar and Percentage Composition
The chapter uses cinnabar as a historical example. The red material was known in different ancient traditions, including as hingula in India. Heating cinnabar was found to yield mercury and sulfur in approximate mass percentages of 86.22% mercury and 13.78% sulfur. The repeated composition is another illustration of definite proportions.
The account also notes that grinding mercury and sulfur together in approximately this mass proportion can form cinnabar, although both materials are toxic and such a process should not be treated as a casual activity.
Using a Mass Ratio
Problem
Sodium chloride contains sodium and chlorine in the mass ratio 23:35.5. If 46 g of sodium reacts completely, how much chlorine is required?
- 1.Write the ratio as sodium : chlorine = 23 : 35.5.
- 2.Notice that 46 g of sodium is twice 23 g.
- 3.Therefore the chlorine mass must also be twice 35.5 g.
- 4.35.5 × 2 = 71 g.
- 5.So 71 g of chlorine is required.
Problem
A compound contains 40% sulfur and 60% oxygen by mass. If a sample contains 20 g of sulfur, how much oxygen must it contain?
- 1.The sulfur-to-oxygen ratio is 40:60.
- 2.Simplify the ratio to 2:3.
- 3.Twenty grams of sulfur corresponds to the '2 parts' side.
- 4.One part is therefore 20 ÷ 2 = 10 g.
- 5.Oxygen occupies 3 parts, so oxygen mass = 3 × 10 = 30 g.
Problem
Carbon monoxide contains carbon and oxygen in the mass ratio 3:4. How much oxygen combines with 9 g of carbon?
- 1.Write carbon : oxygen = 3 : 4.
- 2.Nine grams of carbon is 3 times the 3 g ratio amount.
- 3.Multiply the oxygen side by the same factor: 4 × 3 = 12 g.
- 4.Therefore 12 g of oxygen combines with 9 g of carbon.
Checking Whether Two Results Represent the Same Proportion
Problem
One preparation combines copper and oxygen in the mass ratio 4:1. Another uses 8:2. Do these represent the same proportion?
- 1.Simplify 8:2 by dividing both terms by 2.
- 2.8:2 becomes 4:1.
- 3.Both preparations therefore represent the same copper-to-oxygen mass ratio.
- 4.The results are consistent with a fixed composition for that compound.
Compounds and Mixtures
A compound has its elements chemically combined in a definite composition. A mixture is a physical combination whose components can often be present in different proportions. This is why the Law of Constant Proportions is used for compounds but not for mixtures.
The law is about ratios, not equal masses. A fixed ratio of 1:8 does not mean the masses are the same; it means every valid sample scales both parts together by the same factor.
Quiz
Which description best matches Law of Constant Proportions?
Which term matches this description: In a given compound, the constituent elements are always present in a fixed ratio by mass, irrespective of the source or method of obtaining the compound.
Which statement is a key takeaway from this lesson?
Which additional statement is also a key takeaway from this lesson?
Which further statement is also a key takeaway from this lesson?
Practice Problems
- A pure compound contains elements in a mass ratio 5:2. If 15 g of the first element is present, find the mass of the second.
- Explain why water collected from two different natural sources can contain different impurities but still obey a fixed composition when pure.
- State why a mixture is not expected to obey the Law of Constant Proportions.
- Convert a 25% to 75% composition into its simplest mass ratio.
Key Takeaways
• A pure compound always contains the same elements in a fixed proportion by mass. • This fixed mass ratio remains the same regardless of the amount or source of the compound. • The Law of Constant Proportions applies to pure compounds rather than mixtures. • Mixtures can contain their components in varying proportions.