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In chemistry, understanding how elements combine to form compounds is fundamental. Several laws describe these combinations, such as the Law of Conservation of Mass which states that mass is neither created nor destroyed in a chemical reaction, and the Law of Constant Proportion which tells us that a chemical compound always contains the same elements in the same fixed ratio by mass.
Building on these, the Law of Multiple Proportions provides deeper insight into how the same two elements can combine in different ways to form more than one compound. This law was first proposed by John Dalton in the early 19th century and played a crucial role in the development of atomic theory.
Understanding this law helps us grasp the discrete nature of atoms and how their fixed masses combine in simple ratios to form different substances.
The Law of Multiple Proportions states:
When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers.
To put it simply, if you keep the mass of element A constant, the masses of element B that combine with this fixed mass in different compounds will be simple multiples of each other.
For example, consider two compounds formed by elements A and B:
| Compound | Mass of Element A (g) | Mass of Element B (g) | Ratio of Masses of B (relative to fixed A) |
|---|---|---|---|
| Compound 1 | 10 | 15 | 15 (reference) |
| Compound 2 | 10 | 30 | 30 |
Here, the mass of element A is fixed at 10 g. The masses of element B are 15 g and 30 g in the two compounds. The ratio of these masses is:
This is a simple whole number ratio (2:1), illustrating the law.
This law supports the idea that atoms have fixed masses and combine in whole number ratios. According to Dalton's atomic theory, atoms are indivisible particles with characteristic masses. When elements combine, they do so by joining whole atoms, not fractions of atoms.
For example, carbon monoxide (CO) and carbon dioxide (CO2) both contain carbon and oxygen but in different ratios. The atomic masses of carbon and oxygen are fixed (approximately 12 u for carbon and 16 u for oxygen). The difference in composition arises because molecules contain different numbers of oxygen atoms.
This diagram shows that CO has one oxygen atom per carbon atom, while CO2 has two oxygen atoms per carbon atom. The law of multiple proportions reflects these simple whole number differences in atomic composition.
Step 1: Calculate mass of oxygen combining with a fixed mass of carbon in CO.
In CO, 1 atom of C (12 u) combines with 1 atom of O (16 u).
Fix mass of carbon = 12 g (for simplicity).
Mass of oxygen combining = 16 g.
Step 2: Calculate mass of oxygen combining with the same fixed mass of carbon in CO2.
In CO2, 1 atom of C (12 u) combines with 2 atoms of O (2 x 16 = 32 u).
Fix mass of carbon = 12 g.
Mass of oxygen combining = 32 g.
Step 3: Find the ratio of oxygen masses combining with fixed carbon mass.
\[ \frac{32}{16} = 2 \]
This is a simple whole number ratio, confirming the law.
Answer: The ratio of oxygen masses is 2:1.
Step 1: Fix the mass of nitrogen at 14 g for both compounds.
Mass of oxygen in NO = 16 g
Mass of oxygen in NO2 = 32 g
Step 2: Calculate the ratio of oxygen masses:
\[ \frac{32}{16} = 2 \]
The ratio is a small whole number (2:1), consistent with the law.
Answer: The masses of oxygen that combine with fixed nitrogen are in the ratio 2:1.
Step 1: Fix mass of X = 5 g for both compounds.
Mass of Y in compound 1 = 10 g
Mass of Y in compound 2 = 15 g
Step 2: Calculate ratio of masses of Y:
\[ \frac{15}{10} = 1.5 \]
This is not a whole number, so simplify by dividing both by 5:
10/5 = 2, 15/5 = 3, ratio = 3:2 (after fixing X mass)
Alternatively, express ratio as 3:2 by adjusting fixed mass of X accordingly.
Step 3: Calculate moles of X and Y in each compound.
Step 4: Find mole ratio of Y to X in each compound.
Step 5: Simplify ratio of Y atoms between compounds:
\[ \frac{6}{4} = \frac{3}{2} \]
This is a simple whole number ratio, confirming the law.
Step 6: Determine molecular formulas using mole ratios:
Answer: The ratio of masses of Y is 3:2, and the molecular formulas are XY4 and XY6.
Step 1: Fix mass of M = 8 g for both compounds.
Mass of N in compound 1 = 12 g
Mass of N in compound 2 = 18 g
Step 2: Calculate ratio of masses of N:
\[ \frac{18}{12} = 1.5 \]
Step 3: Simplify ratio to small whole numbers:
1.5 = \(\frac{3}{2}\)
The ratio is 3:2, a simple whole number ratio.
Answer: The masses of N combine with fixed M in the ratio 3:2, confirming the law.
Step 1: Fix mass of A = 10 g for both compounds.
Mass of B in compound 1 = 20 g
Mass of B in compound 2 = 50 g
Step 2: Calculate ratio of masses of B:
\[ \frac{50}{20} = 2.5 \]
Step 3: Simplify ratio to nearest small whole numbers:
2.5 can be expressed as \(\frac{5}{2}\), which is a ratio of 5:2.
This is a ratio of small whole numbers.
Answer: The data obey the law of multiple proportions as the ratio of masses of B is 5:2.
When to use: When comparing masses of elements in different compounds.
When to use: When the ratio is not immediately obvious.
When to use: When direct mass ratios are not in simple whole numbers.
When to use: To avoid confusion with other chemical laws.
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