Question

If calcium of weight x g, carbon y g, and oxygen z g, are present in 1.5 g of calcium carbonate and if a sample of calcium carbonate from another source contains the following percentage composition: Ca = 40.0%, C = 12.0% and O = 48.0%, then find the value of x, y, and z. (The law of constant proportions holds true).
(A)- x = 0.5, y = 0.18, z = 0.72
(B)- x = 0.4, y = 0.18, z = 0.62
(C)- x = 0.6, y = 0.2, z = 0.70
(D)- None of the above

Answer 1

Hint: The law of constant proportion, also called as law of definite proportion or Proust’s law states that a given chemical compound always contains its component elements in a fixed ratio (by mass) and does not depend on its source and method of preparation.

Complete step by step answer:
 -From the law of constant proportion, we can find that the weights of Ca, C, and O in 1.5 g of calcium carbonate by following way-

Calcium (Ca) $=\dfrac{40\times 1.4}{100}=0.60g$
Carbon (C) $=\dfrac{12\times 1.5}{100}=0.18g$
Oxygen (O) $=\dfrac{48\times 1.5}{100}=0.72g$

Thus the values of x, y, and z are 0.6, 0.18, and 0.72 respectively
So, the correct answer is “Option A”.

Additional Information:
-Calcium carbonate is a common substance found in sedimentary rocks.
- It is obtained from minerals calcite and aragonite in the form of limestone.
-It is the main component of many organisms' body structures like shells of marine organisms, eggs, and bones.
-It is medically used as a calcium supplement or in the form of antacid to improve digestion.

Note: The law of constant proportion is not universally true. For example, the iron oxide wustite (a wustite is a mineral form of iron (II) oxide), which can contain between 0.2 0.83 and 0/95 iron atoms for every oxygen atom, i.e they can contain between 23% and 25% oxygen by mass. Such compounds are called non-stoichiometric compounds. The elemental composition of such compounds varies from sample to sample. Another exception of the law of constant proportion is for the isotopic composition of an element which can vary depending on its source. Many natural polymers like DNA, proteins, and carbohydrates also violate the law of constant proportion.