Question

Elements X and Y form two different compounds. In the first 0.324$g$ of X is combined with 0.471$g$ of Y. In second, 0.117$g$ of X combined with 0.509$g$ of Y. State the law illustrated by these chemical combinations.
A.Law of constant proportion
B.Law of multiple proportions
C.Law of reciprocal proportion
D.None of these

Answer 1

Now to give the answer to the above question, we need to know what these laws state, what these are used for as well as their importance. Law of conservation of mass, law of multiple proportions, law of reciprocal proportion and law of constant proportion form the basis of physical chemistry.

Complete step by step solution: First, we will describe each of the given above laws.
The law of constant proportion: This law states that in a compound every element is reacted in a fixed proportion. It is not dependent on the source of the compound or where it is prepared. Every compound is found by combining elements in a fixed ratio of their mass.
Law of multiple proportions: If two elements combine together to form more than one compound. Then when we take a fixed amount of the first element, it reacts with the other element. The ratio of both of them will be a whole number. For example, hydrogen and oxygen form several products when they are combined together.
Law of reciprocal proportions: If an element can be reacted with two different elements, then when those two different elements combine with each other, they do so in a fixed ratio.
Now from studying the above three laws, we can say that the question given above is related to the law of multiple proportions. Because we are given two elements which combine with each other with different ratios.
For two elements combining together to form two different compounds,say ${X_a}{Y_b}$ and ${X_a}{Y_c}$ where ${X_a}$ is taken to be one unit and mass of ${Y_a}$ and ${Y_c}$ is taken as${\mathbf{m}}g$ and ${\mathbf{n}}g$ respectively. The ratio of ${Y_a}$ and ${Y_c}$ should come out as a whole number, only then will the law of multiple proportions hold true.

| Weight of Element X| Weight of Element Y| $\dfrac{Y}{X}$ (amount of Y required by 1$g$ of X )
---|---|---|---
Case1:| 0.324g| 0.471g| 1.45
Case2:| 0.117g| 0.509g| 4.35

We usually fix the weight of one element. Here the weight of X is fixed. So we will see how much X is required in the second case.
0.117$g$ of X requires 0.509$g$ of Y.
Using unitary method,
0.324$g$ of X will require$\dfrac{{0.509}}{{0.117}} \times 0.324 = 1.4095g$of Y
So, we can manipulate row2 of table as follows:

| Weight of Element X| Weight of Element Y
---|---|---
Case1:| 0.324$g$| 0.471$g$
Case2:| 0.324$g$| 1.4095$g$

Now $\dfrac{{Y(case2)}}{{Y(case1)}} = \dfrac{{1.4095}}{{0.471}} = 3$
This value is a whole number that is in account with law of multiple proportions.
So, the correct answer is option B.
Note: The three laws are very important in reaction and formation of compounds. One must remember them and what it states. There are several other laws in chemistry which are important. One such law is the Law of conservation of matter that states matter is always conserved.