Question

An atom of an element ‘X’ is \[1.02\] times heavier than that of an atom of ‘Y’. An atom of ‘Y’ is \[0.1809\] times heavier than that of an atom of oxygen. The atomic mass of ‘X’ is:
A. \[2.952\]
B. \[5.314\]
C. \[4.4\]
D. \[2.6\]

Answer 1

Hint: The atomic mass of an element is the average relative mass of an atom of the element as compared to the mass of \[{}^{{\rm{12}}}{\rm{C}}\]atom taken as \[12\]units.

Complete Step by Step Solution:
A mole is the amount of substance that contains as many particles (atoms, molecules, ions, etc.) as there are atoms exactly in \[{\rm{0}}{\rm{.012}}\,{\rm{kg}}\]\[{\rm{(i}}{\rm{.e}}{\rm{. 12 g)}}\]of carbon \[({}^{{\rm{12}}}{\rm{C)}}\]. It must be remembered that the mass of one mole of an atom is equal to the gram atomic mass of the element, the mass of one mole of a molecule is equal to a gram molecular mass of the substance and the mass of one mole of formula units in case of an ionic compound is equal to gram formula mass of the ionic compound.
As per the given data,
‘Y’ atom is \[0.1809\]times heavier than that of an atom of an oxygen
Mass of one mole of an atom of oxygen is known to be \[{\rm{16}}\,{\rm{g}}\].
Therefore,

Again, element ‘X’ is \[1.02\]times heavier than that of ‘Y’ atom
So,

Hence, atomic mass of ‘X’ is found to be \[{\rm{2}}{\rm{.952}}\,{\rm{g}}\].
Therefore, option A is correct.
Additional information: Gram atomic mass of ana element is defined as the atomic mass of an element in grams or it is the mass in grams which is numerically equal to the atomic mass of an element. For example, the atomic mass of oxygen is \[{\rm{16}}\,{\rm{amu}}\]. Therefore,
\[{\rm{1}}\,\,{\rm{gram}}\,\,{\rm{atom}}\,\,{\rm{of}}\,\,{\rm{oxygen}}\,\,{\rm{ = }}\,{\rm{gram}}\,\,{\rm{atomic}}\,\,{\rm{mass}}\,\,{\rm{of}}\,\,{\rm{oxygen}}\,\,{\rm{ = }}\,\,{\rm{16}}\,{\rm{g}}\].
Number of gram atoms and the mass in grams of an element are related to each other by the relation:
\[{\rm{Number}}\,\,{\rm{of}}\,\,{\rm{gram}}\,\,{\rm{atoms}}\,\,{\rm{ = }}\,\,\dfrac{{{\rm{mass}}\,\,{\rm{in}}\,\,{\rm{grams}}}}{{{\rm{gram}}\,\,{\rm{atomic}}\,\,{\rm{mass}}}}\]

Note: Mole concept is used to calculate the absolute weight of an atom or a molecule, the number of atoms or molecules present in the given mass of a substance, the mass of a given number of atoms or molecules and size of individual atoms or molecules etc.