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**Hint:**Here, we need to find out the atomic weight of an atom of X. For that we will use a unitary method and find out the atomic weight. Formula of a compound tells us about the atoms present in that compound and much more.

**Complete answer:**

Before calculating the atomic weight is X let’s understand what you mean by atomic weight. So, atomic weight, as the name suggests, it’s just the total weight of an atom and atomic weight is due to the presence of neutrons, protons and electrons in it. For example, the atomic weight of carbon which is denoted by $C$ is $12amu$.

Now, let’s calculate the atomic weight of X.

Now, we know that the mass of i mole is equal to its molecular mass.

So, we are given a formula of an acid, that is, $HX{O_2}$, mass of $0.0242$ moles of the acid which is $1.657g$-

So, mass of $0.0242$ moles of acid = $1.657g$

Let’s find out the mass of $1$ mole of acid by dividing $1.657g$ by $0.0242$ moles.

Mass of $1$ mole of $HX{O_2}$= molecular mass of $HX{O_2}$= $\dfrac{{1.657}}{{0.0242}} = 68.47g$

Now, molecular mass of acid = $1 + X + 32$

Since, mass of $1$ mole of $HX{O_2}$= molecular mass of $HX{O_2}$

Therefore,

$\begin{gathered}

1 + X + 32 = 68.47 \\

X = 68.47 - 33 = 35.47 \\

\end{gathered} $

So, the atomic mass of X comes out to be $35.47 \simeq 35.5$ which is of Chlorine.

Therefore, the chemical formula of acid is $HCl{O_2}$ because the atomic weight is $35.5amu$.

**Note:**

Such types of questions look very easy but we often forget this easy relation of moles with their molecular mass. Molecular mass is just the sum of all the atom’s weight multiplied by the number of the same atoms present.

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