Question

Select the correct alternative from the given choices. The number of oxygen atoms present in 2 moles of a compound, which consists of a bivalent metal and a perchlorate ion is (a) \(4 \mathrm{~N}\) (b) \(6 \mathrm{~N}\) (c) \(8 \mathrm{~N}\) (d) \(16 \mathrm{~N}\)

Short answer

Answer: There are \(16 \mathrm{~N}\) oxygen atoms in 2 moles of the compound, where N is Avogadro's number.

Step-by-step solution

Identify the chemical formula for the compound

The compound consists of a bivalent metal (M) and a perchlorate ion (ClO_4^-). Since the metal is bivalent, it will bind with 2 perchlorate ions to form a neutral compound, so the chemical formula for the compound will be M(ClO_4)_2.

Calculate the number of oxygen atoms per formula unit

The perchlorate ions each have 4 oxygen atoms, so in M(ClO_4)_2, we would have 2 * 4 = 8 oxygen atoms.

Calculate the number of oxygen atoms in 1 mole of the compound

Since there are 8 oxygen atoms per formula unit, and 1 mole of the compound contains Avogadro's number (N) of formula units, there will be 8 * N oxygen atoms in 1 mole of the compound.

Calculate the number of oxygen atoms in 2 moles of the compound

Now, we need to find the number of oxygen atoms in 2 moles of the compound. Since there are 8 * N oxygen atoms in 1 mole, there will be 2 * 8 * N = 16 * N oxygen atoms in 2 moles of the compound. So, the correct alternative is (d) \(16 \mathrm{~N}\).

Key concepts

Bivalent Metal

A bivalent metal is a metal that typically forms ions with a +2 charge. This means that in chemical reactions, the metal loses two electrons to form a stable cation. The significance of a bivalent metal lies in its ability to form compounds requiring two anions for charge balance. This aspect is critical when understanding the compound formation like in the question where a bivalent metal forms a bond with perchlorate ions.

• Examples of bivalent metals include calcium (Ca), magnesium (Mg), and iron (Fe)
• Bivalency results from the metal achieving a more stable electron configuration after losing two electrons

This property influences how they interact with other ions to create neutral compounds.

Perchlorate Ion

The perchlorate ion is a polyatomic ion with the formula \(ClO_4^-\). It consists of one chlorine atom bonded to four oxygen atoms. The entire ion carries a -1 charge, indicating that it's an anion.

• The perchlorate ion is quite stable and commonly found in salts such as sodium perchlorate
• In the given chemical compound, each ion contributes four oxygen atoms

Understanding the configuration of perchlorate ions helps explain how they form compounds with cations from bivalent metals.

Oxygen Atoms Calculation

The calculation of oxygen atoms in chemical compounds involves understanding the ratio of ions in the formula. For the compound M(ClO_4)_2, calculate the number of oxygen atoms present:The perchlorate ion, \(ClO_4^-\), contains 4 oxygen atoms. Thus, in M(ClO_4)_2, there are 2 perchlorate ions. The total number of oxygen atoms becomes: \[ 2 \times 4 = 8 \text{ oxygen atoms per formula unit} \] When solving for moles, Avogadro's number \(N\) is used to denote the number of units in a mole, leading to 8\(N\) oxygen atoms per mole. In the problem where two moles are considered:\[ 2 \times 8 \times N = 16N \text{ oxygen atoms in 2 moles} \] This systematic approach helps understand how molecular formula influences the total number of constituent atoms.

Neutral Compound Formation

Neutral compound formation is the process of combining ions such that the total charge of the compound is zero. For compounds with bivalent metals and perchlorate ions, the formation requires balancing the charges. In this case, a bivalent metal, which generally holds a +2 charge, pairs with two perchlorate ions, each carrying a -1 charge. This results in a neutral compound as follows:

• Metal cation: \(M^{2+}\)
• Two perchlorate anions: \(2 \times (ClO_4^-)\)

Thus, the chemical formula M(ClO_4)_2 forms perfectly, maintaining overall neutrality because the charges from the metal and the perchlorates balance each other out, ultimately fulfilling stoichiometry principles.