Question

Two elements \(\mathrm{X}\) (atomic weight \(=75\) ) and \(\mathrm{Y}\) (atomic weight \(=16\) ) combine to give a compound having \(75.8 \% \mathrm{X}\). The formula of the compound is: (a) \(\mathrm{X}_{2} \mathrm{Y}_{2}\) (b) \(\mathrm{X}_{2} \mathrm{Y}_{3}\) (c) \(\mathrm{X}_{2} \mathrm{Y}\) (d) XY

Short answer

The formula of the compound is \( \mathrm{X}_2 \mathrm{Y}_3 \).

Step-by-step solution

Calculate Mass Ratio per 100g of Compound

Since we have 75.8% of element \(X\), this means in 100 grams of the compound, 75.8 grams is \(X\) and the rest is \(Y\). To find the mass of \(Y\):\[\text{Mass of } Y = 100 - 75.8 = 24.2 \text{ grams}\]

Calculate Moles of Each Element

Now, convert the masses of \(X\) and \(Y\) into moles using their atomic weights. For \(X\): \[\text{Moles of } X = \frac{75.8}{75} \approx 1.01 \]For \(Y\): \[\text{Moles of } Y = \frac{24.2}{16} \approx 1.51 \]

Determine the Simplest Mole Ratio

To find the simplest ratio of atoms in the compound, we divide each element's moles by the smallest number of moles:For \(X\): \[\frac{1.01}{1.01} = 1\]For \(Y\): \[\frac{1.51}{1.01} \approx 1.5\]

Deduce the Empirical Formula

The simplest whole number ratio corresponding to \(1:1.5\) is \(2:3\) when multiplied by 2 to eliminate the fraction. Thus, the empirical formula of the compound is \(X_2Y_3\).

Key concepts

Empirical Formula

An empirical formula is a way to express the simplest integer ratio of atoms present in a compound. It does not give the exact number of atoms but rather the simplest whole-number ratio. For example, in our exercise, we calculated the smallest integer ratio of atoms for the compound made from elements X and Y. By converting the mass of each element to moles and finding their ratio, the empirical formula was deduced to be \(X_2Y_3\). This formula shows that for every 2 atoms of X, there are 3 atoms of Y in the compound.

Mass Ratio Calculation

Mass ratio calculation is a method to determine how much of each element is present in a compound based on their masses. This is crucial when trying to identify the empirical formula. To find the mass ratio, you start with the percentage composition of the compound. For instance, if a compound has 75.8% X, within a 100-gram sample, this translates to 75.8 grams of X. The remainder, which is 24.2 grams, would be element Y. Knowing each element's mass helps convert these masses to moles.

Mole Concept

The mole concept is a fundamental idea in chemistry that allows chemists to count atoms, molecules, or particles by relating them to a measurable mass. One mole of any substance contains Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\). Using their atomic weights, we converted the masses of X and Y into moles: \(\frac{75.8}{75} = 1.01\) moles of X and \(\frac{24.2}{16} = 1.51\) moles of Y. This mole conversion is key to simplifying the ratio of the elements in the compound.

Atomic Weight

Atomic weight, or atomic mass, is the average mass of an atom of an element, measured in atomic mass units (amu). It reflects the average mass of an element's isotopes, weighted by their natural abundance. In calculations involving empirical formulas, atomic weights are used to convert mass to moles. In this exercise, X and Y have atomic weights of 75 and 16, respectively. These values were vital in our calculations to convert the percentage of each element in the compound into moles, which ultimately led to the determination of the empirical formula.