Problem 47 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

The formula is \( \text{X}_2\text{Y}_3 \).

Step 1: Determine the Mass of the Compound

Assume you have 100 grams of the compound, which contains 75.8 grams of \( \text{X} \) and \( 24.2 \) grams of \( \text{Y} \), since \( 100 - 75.8 = 24.2 \).

Step 2: Calculate Moles of X in the Compound

Calculate the moles of \( \text{X} \) using its atomic weight:\[\text{Moles of X} = \frac{75.8}{75} = 1.01\text{ moles}\]

Step 3: Calculate Moles of Y in the Compound

Calculate the moles of \( \text{Y} \) using its atomic weight:\[\text{Moles of Y} = \frac{24.2}{16} = 1.5125\text{ moles}\]

Step 4: Determine the Simplest Whole Number Ratio

Divide both amounts by the smallest number of moles to convert them into a simple whole number ratio:\[\text{Ratio of X} = \frac{1.01}{1.01} = 1\]\[\text{Ratio of Y} = \frac{1.5125}{1.01} \approx 1.5\]

Step 5: Converting to Integer Subscripts

The ratio \(1:1.5\) suggests multiplying through by 2 to achieve whole numbers:\[\text{X: } 1 \times 2 = 2\]\[\text{Y: } 1.5 \times 2 = 3\]Thus, the formula is \( \text{X}_2\text{Y}_3 \).

Key Concepts

Stoichiometry

Stoichiometry is like a recipe in chemistry. It helps us find out how much of each ingredient (or element) is needed to make a chemical compound.
Imagine you're baking a cake: you need the right amounts of flour, sugar, and eggs. Similarly, stoichiometry helps chemists figure out the right amounts of elements to combine and form a compound.

• It works by using relationships found in chemical equations.
• These equations show how elements or compounds react and form products.

In our example, we're given a percentage of elements in a compound and need to understand how these amounts come together to form a chemical formula. By understanding stoichiometry, we can calculate the exact quantities of each element required to make the compound, ensuring balance and correctness.

Mole Concept

The mole concept is a vital part of chemistry that carries the same significance as using a dozen in everyday life. It measures substances not by weight, but by number of entities, like atoms or molecules.

• One mole is a standard count of 6.022 x 10²³ entities, known as Avogadro's number.
• Using this count, we can relate the mass of a substance to the amount of atoms or molecules it contains.

In our problem, the atomic weights of elements X and Y guide us in calculating how many moles of each element are present in 100 grams of the compound.
This helps us figure out the simplest whole number ratio between them, much like counting eggs for a recipe if you have the total weight but need to know the number of eggs.

Empirical Formula Calculation

An empirical formula shows the simplest ratio of elements in a compound and is determined through calculation.

• We start by converting the mass of each element to moles, using their atomic weights.
• Next, we find the simplest ratio of these moles by dividing by the smallest amount calculated.
• Finally, we convert these ratios into whole numbers to find the empirical formula.

In the exercise, we discover a compound with a ratio of X to Y that doesn't immediately give whole numbers: 1:1.5. By multiplying through by 2, we translate this into a whole number ratio of 2:3.
Thus, the empirical formula, representing the simplest whole number ratio of the elements in the compound, emerges as \( \text{X}_2\text{Y}_3 \). This formula confirms the proportion of X and Y essential for forming the compound.