Problem 68 - A Complete Resource Book in Chemistry for JEE Main

Question

The percentage weight of \(\mathrm{Zn}\) in white vitriol \(\left[\mathrm{ZnSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\right]\) is approximately equal to \((\mathrm{Zn}=65\) \(\mathrm{S}=32, \mathrm{O}=16\) and \(\mathrm{H}=1\) ) (a) \(21.56 \%\) (b) \(32.58 \%\) (c) \(22.65 \%\) (d) \(26.55 \%\)

Step-by-Step Solution

Answer

The percentage weight of Zn in white vitriol is approximately 22.65%, matching option (c).

Step 1: Calculate Molar Mass of ZnSO_4.7H_2O

Calculate the molar mass of the compound \( \text{ZnSO}_4 \cdot 7 \text{H}_2\text{O} \). \[ \text{Molar mass} = \text{Zn} + \text{S} + 4 \times \text{O} + 7 \times (2\times\text{H} + \text{O}) \] Values: \( \text{Zn} = 65, \text{S} = 32, \text{O} = 16, \text{H} = 1 \). Calculate each part: Zn = 65, S = 32, O for SO_4 = 4\times16 = 64, 7\times(2 \times 1 + 16) = 126. \[ \text{Total} = 65 + 32 + 64 + 126 = 287 \] Thus, the molar mass of ZnSO_4.7H_2O is 287 g/mol.

Step 2: Calculate Zn Percentage

Calculate the percentage of Zn in ZnSO_4.7H_2O using the formula: \[ \text{Percentage of Zn} = \left( \frac{\text{Atomic Mass of Zn}}{\text{Molar Mass of } \text{ZnSO}_4 \cdot 7\text{H}_2\text{O}} \right) \times 100 \] \[ \text{Percentage of Zn} = \left( \frac{65}{287} \right) \times 100 \approx 22.65\% \]

Step 3: Select the Correct Option

Compare the calculated percentage of Zn to the given options: (a) 21.56%, (b) 32.58%, (c) 22.65%, (d) 26.55%. The calculated value is approximately 22.65%, which matches option (c).

Key Concepts

Percentage Composition

The notion of percentage composition refers to the percent by mass of each element in a chemical compound. It tells us how much of each element is present in a given amount of the compound. To find the percentage composition of an element, you calculate the ratio of the mass of the element to the total molar mass of the compound, and then multiply by 100 to get a percentage.
For example, in the compound \(\mathrm{ZnSO}_{4} \cdot 7\mathrm{H}_{2}\mathrm{O}\), if we want to calculate the percentage of zinc (\(\mathrm{Zn}\)), we use the atomic mass of zinc and the molar mass of the entire compound. After finding the molar mass of \(\mathrm{ZnSO}_{4} \cdot 7\mathrm{H}_{2}\mathrm{O}\) as 287 g/mol, the percentage of zinc is calculated as follows:

• Take the atomic mass of zinc which is 65 g/mol.
• Divide by the molar mass of the compound: \(\frac{65}{287}\).
• Multiply by 100 to convert into a percentage: \(\left(\frac{65}{287}\right) \times 100 \approx 22.65\%%\).

Understanding percentage composition is very useful in various applications, such as determining the nutritional values of compounds or calculating reagents needed for a reaction.

Chemical Formula

A chemical formula provides a clear structure depicting the composition of a molecule or compound. It includes the symbols of the elements involved, along with numbers denoting the quantity of each type of atom present. It serves as a shorthand way of describing the type and number of atoms in a molecule.
Take for instance, the chemical formula of white vitriol, \(\mathrm{ZnSO}_{4} \cdot 7\mathrm{H}_{2}\mathrm{O}\). This indicates a compound formed by zinc (\(\mathrm{Zn}\)), sulfur (\(\mathrm{S}\)), and oxygen (\(\mathrm{O}\)), along with water molecules (\(\mathrm{H}_{2}\mathrm{O}\)).

• \(\mathrm{ZnSO}_{4}\) identifies the basic sulfate structure where zinc is bound to the sulfate ion \((\mathrm{SO}_{4}^{2-})\).
• \(7\mathrm{H}_{2}\mathrm{O}\) suggests there are seven water molecules attached, a characteristic of hydration in salts.

Recognizing and interpreting chemical formulas is crucial for understanding the composition and stoichiometry of compounds, allowing chemists to envisage the arrangement and relative quantities of atoms.

Atomic Mass Calculation

Atomic mass calculation is a fundamental part of understanding how much of each element is present in a compound. The atomic mass of an element is effectively the mass of a "typical" atom of that element. It is expressed in atomic mass units (amu) or grams per mole (g/mol), which allows us to relate amounts on the atomic scale to real-world amounts of material.
In a compound like \(\mathrm{ZnSO}_{4} \cdot 7\mathrm{H}_{2}\mathrm{O}\), you need to add up the atomic masses of all constituent atoms to find the total molar mass. For instance:

• Zinc (\(\mathrm{Zn}\)) has an atomic mass of 65 g/mol.
• Sulfur (\(\mathrm{S}\)) is 32 g/mol.
• Each oxygen (\(\mathrm{O}\)) atom is 16 g/mol, in \(\mathrm{SO}_{4}\) there's 4×16 = 64 g/mol.
• The water component (7 \(\times\) (2\(\mathrm{H}\) + \(\mathrm{O}\))) contributes 126 g/mol, with each hydrogen being 1 g/mol.

Add these numbers to obtain the full molar mass of the compound: 65 + 32 + 64 + 126 = 287 g/mol. Accurate atomic mass calculations are important for determining the precise composition and reactivity of compounds in any chemical context.