Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

A compound contains atoms \(X, Y, Z\) the oxidation number of \(\mathrm{X}\) is \(+2, \mathrm{Y}\) is \(+5\) and \(\mathrm{Z}\) is \(-2\) The possible form of the compound is (a) \(\mathrm{XY}_{1} \mathrm{Z}_{2}\) (b) \(\mathrm{Y}_{2}\left(\mathrm{XZ}_{3}\right)_{2}\) (c) \(\mathrm{X}_{3}\left(\mathrm{YZ}_{4}\right)_{2}\) (d) \(\mathrm{X}_{3}\left(\mathrm{Y}_{4} \mathrm{Z}\right)_{2}\)

Step-by-Step Solution

Answer

The possible form of the compound is option (c) X3(YZ4)2.

Step 1: Understand Oxidation Numbers

We are given that atoms X, Y, and Z have oxidation numbers of +2, +5, and -2 respectively. This means that in the compound, X contributes +2 to the total charge, Y contributes +5, and Z contributes -2.

Step 2: Establish the Charge Balance Equation

For a compound to be neutral, the total charge must equal zero. Therefore, we need to find a combination of these atoms where the sum of their oxidation numbers is zero.

Step 3: Test Option (a) XY1Z2

Calculate the total oxidation number: +2 (from X) \(\times 1\) + +5 (from Y) \(\times 1\) + -2 (from Z) \(\times 2\) = 2 + 5 - 4 = 3. This does not equal zero, so the compound is not neutral.

Step 4: Test Option (b) Y2(XZ3)2

Calculate the total oxidation number: +5 (from Y) \(\times 2\) + \[(+2 \times 1 + -2 \times 3)\] \(\times 2\). Simplifying, the part inside the brackets yields: +2 - 6 = -4. Thus, the total charge is +10 + \(2 \times (-4) = +10 - 8 = +2\). This does not equal zero, so the compound is not neutral.

Step 5: Test Option (c) X3(YZ4)2

Calculate the total oxidation number: +2 (from X) \(\times 3\) + \[(+5 \times 1 + -2 \times 4)\] \(\times 2\). Simplifying, the part inside the brackets yields: +5 - 8 = -3. Thus, the total charge is +6 + \(2 \times (-3) = +6 - 6 = 0\). This equals zero, so the compound is neutral.

Step 6: Test Option (d) X3(Y4Z)2

Calculate the total oxidation number: +2 (from X) \(\times 3\) + \[(+5 \times 4 + -2 \times 1)\] \(\times 2\). Simplifying, the part inside the brackets yields: +20 - 2 = +18. The total charge is +6 + \(2 \times 18 = +6 + 36 = +42\). This does not equal zero, so the compound is not neutral.

Step 7: Conclusion

Out of all the options, only option (c) X3(YZ4)2 provides a neutral compound where the total oxidation number is zero.

Key Concepts

Charge balance

When forming chemical compounds, it is crucial to understand the concept of charge balance. This principle is based on the idea that compounds must have an overall net charge of zero to be stable.
It means that the sum of the oxidation numbers coming from each type of atom in the compound must equal zero.

Oxidation numbers, for example, indicate how many electrons an atom gains or loses when forming a compound.
For the compound to be neutral, you must have a harmonic balance between the positive and negative contributions of these oxidation numbers.

• If X has an oxidation number of +2, it contributes +2 to the charge.
• If atom Y is +5, it contributes +5.
• Z, with -2, contributes -2 per each atom.

The total of these contributions must sum up to zero for the compound to achieve charge balance. This is a fundamental concept in chemistry to ensure the stability and formation of a compound.

Neutral compound

A neutral compound is one where the overall electrical charge is zero.
This neutrality results from a perfect balance between the positive and negative charges in the compound.
For students, it is vital to understand that each atom in a compound contributes to the overall charge with its oxidation number.

To achieve a neutral compound:

• Positive oxidation numbers should be counteracted by negative ones.
• The sum of all oxidation numbers within the compound must equal zero for the compound to be stable and neutral.

For example, if we calculate the option (c) X extsubscript{3}(YZ extsubscript{4}) extsubscript{2}, with the oxidation numbers +2 for X, +5 for Y, and -2 for Z:

• The three X atoms contribute a total of +6.
• Within the parentheses with 2 units, Y contributes +5 and four Z atoms contribute -8, yielding -3 per set, for a total of -6.
• Therefore, +6 and -6 cancel out, achieving a net charge of 0.

This option results in a neutral compound, illustrating the peaceful balance required for chemical stability.

Chemical formula determination

Determining a chemical formula involves finding the correct ratio of atoms that fulfills the requirement of a neutral compound.
This often requires a careful calculation, using oxidation numbers as a guide.
Once you know the oxidation states of each atom, you can set up equations to determine how many of each atom should be present to form a neutral compound.

In our exercise, we had to determine which formula, out of several options, resulted in a neutral compound:

• First, check each option by calculating the total charge.
• For X extsubscript{3}(YZ extsubscript{4}) extsubscript{2}, combine the charges as explained to see if they yield zero.
• If the total charge equals zero, then the formula is correct and represents a neutral compound.

Pay close attention to the problem statement and understand each atom's oxidation state.
By only selecting the combination where all charges add to zero, you correctly determine the chemical formula.
This practice sharpens your chemistry skills and enhances your ability to solve similar exercises effectively.