Question

Let A, B and C be three different elements such that one part of A combines with two parts of B and that six parts of C combine with 4 parts of B. If A and C were to combine, then their ratio of their masses will be governed by:
a.) Law of Definite Proportions
b.) Law of Multiple Proportions
c.) Law of Reciprocal Proportions
d.) Law of Conservation of Mass

Answer 1

Hint: Try and remember the definitions of all of the chemical laws given in the options and try to think how many of them are irrelevant to this question. The process of elimination is a fairly helpful way to solve this question.

Complete step-by-step answer:
To find the answer to this question, let us go through the definitions and examples of each of the given options and see which one is relevant to this case.

a) Law of Definite Proportions: In chemistry, the law of definite proportion, states that a given chemical compound always contains its component elements in fixed ratio (by mass) and does not depend on its source and method of preparation.
For example, oxygen makes up about 8/9 of the mass of any sample of pure water, while hydrogen makes up the remaining 1/9 of the mass.

b) Law of Multiple Proportions: The law of multiple proportions states that if two elements form more than one compound between them, then the ratios of the masses of the second element which combine with a fixed mass of the first element will always be ratios of small whole numbers.
For example, let us compare ethane ($C_2H_6$) with propane ($C_3H_8$). The weight of hydrogen which combines with 1 g carbon is 0.252 g in ethane and 0.224 g in propane. The ratio of those weights is 1.125, which can be expressed as the ratio of two small numbers 9:8.

c) Law of Reciprocal Proportions: If two different elements combine separately with a fixed mass of a third element, the ratio of the masses in which they do so are either the same as or a simple multiple of the ratio of the masses in which they combine with each other.
For example, 3 g of C reacts with 1 g of H to form methane.
Also, 8 g of O reacts with 1 g of H to form water.
The mass ratio of C:O = 3:8
In the same way, 12 g of C reacts with 32 g of O to form $CO_2$.
The mass ratio of C:O = 12:32 = 3:8

The mass ratio in which C and O combine with each other is the same as the mass ratio in which they separately combine with a fixed mass of H.

d) Law of Conservation of Mass: The law of conservation of mass states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations.
According to the law of conservation of mass, the mass of the products in a chemical reaction must equal the mass of the reactants.
Now, looking at this question,
A combines with B in the ratio 1:2
C combines with B in the ratio 3:2
$\therefore$ A and C combine in the ratio 1:3

As this conversion is directly according to the law of reciprocal proportion, therefore the answer is c).

NOTE: Immense clarity regarding laws involving chemical combination is required to try and solve this question. Also be very careful while working with ratios and proportions in this question as the slightest bit of carelessness could result in the reciprocal of the required answer.