Read the passage given below and answer the following questions:
The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. The experimental approach required the introduction of a new unit for the number of substances, the mole, which remains indispensable in modern chemical science. A mole is an amount unit similar to familiar units like pair, dozen, gross, etc. It provides a 

specific measure of the number of atoms or molecules in a bulk sample of matter.
A mole is defined as the amount of substance containing the same number of discrete entities (atoms, molecules, ions, etc.) as the number of atoms in a sample of pure ${ }^{12} \mathrm{C}$ weighing exactly $12 \mathrm{~g}$. One Latin connotation for the word "mole" is "large mass" or "bulk," which is consistent with its use as the name for this unit.

The mole provides a link between an easily measured macroscopic property, bulk mass, and an extremely important fundamental property, the number of atoms, molecules, and so forth.
The number of entities composing a mole has been experimentally determined to be $6.02214179 \times 10236.02214179 \times 1023$, a fundamental constant named Avogadro's number $\left(N_A\right)$ or the Avogadro constant in honor of Italian scientist Amedeo Avogadro. This constant is properly reported with an explicit unit of "per mole," a conveniently rounded version being $6.022 \times 1023 / \mathrm{mol}$ $6.022 \times 1023 / \mathrm{mol}$.
Consistent with its definition as an amount unit, 1 mole of any element contains the same number of atoms as 1 mole of any other element. The masses of 1 mole of different elements, however, are different, since the masses of the individual atoms are drastically different.

The molar mass of an element (or compound) is the mass in grams of 1 mole of that substance, a property expressed in units of grams per mole $(\mathrm{g} / \mathrm{mol})$.
The following questions (i-iv) are multiple choice questions. Choose the most appropriate answer :
(i) A sample of copper sulfate pentahydrate contains $8.64 \mathrm{~g}$ of oxygen. How many grams of $\mathrm{Cu}$ is present in the sample?
(a) $0.952 g$
(b) $3.816 \mathrm{~g}$
(c) $3.7829$
(d) $8.649$

(ii) A gas mixture contains $50 \%$ helium and $50 \%$ methane by volume. What is the per cent by weight of methane in the mixture?
(a) 19.97\%
(b) $20.05 \%$
(c) $50 \%$
(d) $80.03 \%$
(iii) The mass of oxygen gas which occupies $5.6$ litres at STP could be
(a) gram atomic mass of oxygen
(b) one fourth of the gram atomic mass of oxygen
(c) double the gram atomic mass of oxygen
(d) half of the gram atomic mass of oxygen
(iv) What is the mass of one molecule of yellow phosphorus? (Atomic mass of phosphorus $=30$ )
(a) $1.993 \times 10^{-22} \mathrm{mg}$
(b) $1.993 \times 10^{-19} \mathrm{mg}$
(c) $4.983 \times 10^{-20} \mathrm{mg}$
(d) $4.983 \times 10^{-23} \mathrm{mg}$
Or
The number of moles of oxygen in $1 \mathrm{~L}$ of air containing $21 \%$ oxygen by volume, in standard conditions is
(a) $0.186 \mathrm{~mol}$
(b) $0.21 \mathrm{~mol}$
(c) $2.10 \mathrm{~mol}$
(d) $0.0093 \mathrm{~mol}$