Problem 158 - A Complete Resource Book in Chemistry for JEE Main

Question

Equivalent weight of a metal is \(4.5\) and the molecular weight of the chloride is \(80 .\) The valency of the metal is ___ .

Step-by-Step Solution

Answer

The valency of the metal is 18.

Step 1: Understanding Equivalent Weight

The equivalent weight of a metal is defined as the mass of the metal that combines with or displaces 1 gram of hydrogen or equivalent amounts of another element. The formula used is \( \text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{Valency}} \). Here, the equivalent weight of the metal is given as 4.5.

Step 2: Using the Formula

Given the molecular weight of the metal chloride is 80, we set up the equation: \( 4.5 = \frac{80}{\text{Valency}} \). This equation comes from rearranging the formula for equivalent weight to solve for valency: \( \text{Valency} = \frac{\text{Molecular weight}}{\text{Equivalent weight}} \).

Step 3: Solving for Valency

Now, solve the equation \( 4.5 = \frac{80}{\text{Valency}} \). By multiplying both sides by the valency, we have: \( 4.5 \times \text{Valency} = 80 \). Then, solve for valency by dividing both sides by 4.5: \( \text{Valency} = \frac{80}{4.5} \).

Step 4: Final Calculation

Perform the final calculation: \( \text{Valency} = \frac{80}{4.5} \approx 17.78 \). Since valency must be a whole number, round to the nearest whole number to find the valency of the metal.

Key Concepts

Understanding Equivalent Weight

Equivalent weight is a fundamental concept in chemistry, especially when dealing with reactions and compounds. It refers to the mass of a substance that will react with or displace a fixed quantity of another element, typically hydrogen. Think of it as a way to measure how much of one element will swap with another in a chemical reaction.

For metals, the equivalent weight can be determined by the formula:

• Equivalent weight = \( \frac{\text{Molecular weight}}{\text{Valency}} \)

This equation implies you can find the equivalent weight if you know the molecular weight and the valency of a substance.

In the context of the exercise, the equivalent weight of the metal was already known (4.5), providing a stepping stone to find its valency.

Exploring Molecular Weight

Molecular weight is another key aspect of understanding chemical compounds. It’s the sum of the atomic weights of all the atoms in a molecule. For metal chlorides, it tells us how heavy the molecule is.

To calculate molecular weight, you sum the weights of each atom in the compound, found on the periodic table. For instance:

• A molecule of water, \( H_2O \), has molecular weight computed from two hydrogen atoms and one oxygen atom.

Molecular weight is expressed in atomic mass units (amu) and gives insights into the size and scale of the particle involved.

In our exercise, the given molecular weight of the metal chloride was 80, setting the stage to use it alongside equivalent weight for calculating valency.

Understanding Metal Chloride

Metal chlorides are compounds formed between metals and chlorine. They typically occur when a metal donates electrons to a chlorine atom, forming a stable compound. These are common in chemistry due to the reactive nature of chlorine.

Let's examine the typical characteristics of metal chlorides:

• They generally dissolve in water, producing a basic solution.
• They have various uses in industry, like in water treatment and purification.
• They often form simple binary compounds, yet can vary in structure and complexity.

Understanding the basics of metal chloride is crucial because it gives insight into the compounds used in reactions, in this case, helping determine the valency of the metal when combined with chlorine.