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# $2.40g$ of the element $Z$ combines exactly with $1.6g$ of oxygen to form a compound with the formula $Z{O_2}$. What is the relative atomic mass of $Z$?(A) $24.0$(B) $32.0$(C) $48.0$(D) $64.0$

Last updated date: 16th Sep 2024
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Hint: We know that $1$ mole contains a fixed number of particles and it is the definite amount of a substance which can be expressed in terms of weight, volume and number of particles and we also know that relative atomic mass is the average mass of atoms compared to $\dfrac{1}{{12}}th$ the mass of carbon-$12$atom.

Complete Step by step answer:We are aware with the fact that $1$ mole contains a fixed number of particles and it is the definite amount of a substance which can be expressed in terms of weight, volume and number of particles and we also know that relative atomic mass is the average mass of atoms compared to $\dfrac{1}{{12}}th$ the mass of carbon-$12$ atom.
As given in the question, mass of oxygen is $1.6g$ and we know the molecular mass of oxygen as well which is $16g$, so we can now calculate the moles of oxygen using this:
$moles = \dfrac{{mass}}{{molecular\;mass}}$
$\Rightarrow moles = \dfrac{{1.6}}{{16}} \\ \Rightarrow moles\;of\;oxygen = 0.1mol \\$
From the given formula, $Z{O_2}$, we know that oxygen combines with element $Z$ in a ratio $1:2$, so we can say that number of moles of $Z$$= 0.5mol$.
Now, using these moles and the given mass of the element we can easily calculate the atomic mass:
$moles = \dfrac{{mass}}{{molecular\;or\;atomic\;mass}}$
$\Rightarrow 0.05 = \dfrac{{2.4}}{{at.mass}}$
$\Rightarrow atomic\;mass = \dfrac{{2.4}}{{0.5}} \\ \Rightarrow atomic\;mass = 48g \\$
Or relative atomic mass $= 48$as it is a dimensionless quantity.

Therefore the correct answer is (C).

Note: A relative atomic mass is basically the ratio of the mean of average atomic mass of all atoms of an element in a given sample and it is considered relative to that of carbon-$12$. That is why relative atomic mass is a dimensionless quantity.