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An oxide of arsenic contains \[65.2\% \] arsenic by weight. What will be its simplest formula?

Last updated date: 22nd Jun 2024
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Hint: To answer this question we must need to know the definition for the percentage composition and number of moles. The value of mass can be calculated from the mole concept and hence number of moles from the percentage composition.

Formula used: \[{\text{number of mole (n) = }}\dfrac{{{\text{mass of substance}}}}{{{\text{Molar mass}}}}\]

Complete step by step solution:
Percentage composition can be defined in two ways percentage by mass and percentage by volume. Since we have not been specified so we will consider it as a percentage by mass. Mass percentage is defined as the mass of substance present in the 100 g of solution.
We have been given that the percentage of arsenic is \[65.2\% \]. Since the percentage is always calculated from 100, so we will get the percentage of oxygen as,
\[100 - 65.2\% = 34.8\% \]
So this means that \[65.2\% \] arsenic by mass means \[65.2\] g of arsenic is present in the 100 g of solution and \[34.8\% \] Oxygen by mass means \[34.8\] g of oxygen is present in the 100 g of solution.
The molar mass of arsenic is 75 amu and that of oxygen is 16 amu.
We will calculate the number of moles from the above formula:
\[{{\text{n}}_{{\text{Ar}}}} = \dfrac{{65.2}}{{75}} = 0.869{\text{ mole}}\]
\[{{\text{n}}_{\text{O}}} = \dfrac{{34.8}}{{16}} = 2.175{\text{ mole}}\]
Hence, the ratio of these elements in the given mixture will be :
\[{\text{Ar : O}} = 0.869:2.175\]
We need to convert this in whole numbers because elements cannot be in fraction in a compound. Hence we will divide all the ratio with \[0.869\], we will get \[{\text{Ar : O}} = 1:2.5\] , we need to multiply it with 2 to convert it into whole number and hence we will get the ratio as \[{\text{Ar : O}} = 2:5\]. This means there is 2 arsenic atom and 5 oxygen atom and hence the formula will be \[{\text{A}}{{\text{s}}_2}{{\text{O}}_5}\].
Hence the correct option is D.

Note: Empirical formula represents the small positive integer value in which atoms are present in any compound. It does not mention the arrangement of atoms in any way. The molecular formula exactly depicts the number of atoms as well as their proper arrangements of atoms in a formula. It is possible that two compounds may have similar empirical formula but the molecular formula is unique for each compound.