Identical red balls, each weighing 2 g, are contained in a box and are labeled as A. Another box contains identical blue colored balls, labelled as B, each weighing 5 g. Which of the following combinations applies: AB, AB₂, A₂B, and A₂B₃?

Law of multiple proportion

The correct answer is option 2. Law of multiple proportion.

The Law of Multiple Proportions, formulated by John Dalton in the early 19th century, states that when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in ratios of small whole numbers.

In the given scenario, we have two different types of balls: red balls labeled as \(A\), each weighing \(2 \, \text{g}\), and blue balls labeled as \(B\), each weighing \(5 \, \text{g}\). Let's consider the different combinations:

1. \(AB\): If one red ball (\(A\)) combines with one blue ball (\(B\)), the total mass would be \(2 \, \text{g} + 5 \, \text{g} = 7 \, \text{g}\).
2. \(AB_2\): If one red ball (\(A\)) combines with two blue balls (\(B\)), the total mass would be \(2 \, \text{g} + (2 \times 5 \, \text{g}) = 12 \, \text{g}\).
3. \(A_2B\): If two red balls (\(A\)) combine with one blue ball (\(B\)), the total mass would be \((2 \times 2 \, \text{g}) + 5 \, \text{g} = 9 \, \text{g}\).
4. \(A_2B_3\): If two red balls (\(A\)) combine with three blue balls (\(B\)), the total mass would be \((2 \times 2 \, \text{g}) + (3 \times 5 \, \text{g}) = 16 \, \text{g}\).

We can observe that the masses of the elements (balls) that combine in different ratios (combinations) are in ratios of small whole numbers: \(1:1\), \(1:2\), \(2:1\), and \(2:3\), respectively. This illustrates the Law of Multiple Proportions.

Therefore, the given scenario exemplifies the concept of the Law of Multiple Proportions, as the masses of the elements combine in ratios of small whole numbers when forming different compounds (combinations).