Problem 18 - Chemistry for Allied Health

Question

How many equivalents are there in \(2.0\) moles of the ion of each element below? a. magnesium b. aluminum c. sulfur d. bromine (Br) e. cesium (Cs) f. barium (Ba)

Step-by-Step Solution

Answer

a) 4.0 equivalents; b) 6.0 equivalents; c) 4.0 equivalents; d) 2.0 equivalents; e) 2.0 equivalents; f) 4.0 equivalents.

Step 1: Understanding Equivalents

Equivalent is a measure of the reactive capacity of a molecule, similar to moles. For ions, the number of equivalents can be found by multiplying the number of moles by the valence of the ion. Valence is the charge on the ion.

Step 2: Magnesium Equivalents

Magnesium often forms a +2 ion, giving it a valence of 2. To find equivalents, multiply the moles by the valence: \(2.0 \text{ moles} \times 2 = 4.0 \text{ equivalents}\).

Step 3: Aluminum Equivalents

Aluminum typically forms a +3 ion, so the valence is 3. Therefore, \(2.0 \text{ moles} \times 3 = 6.0 \text{ equivalents}\).

Step 4: Sulfur Equivalents

Sulfur can form a -2 ion, thus having a valence of 2. Thus, \(2.0 \text{ moles} \times 2 = 4.0 \text{ equivalents}\).

Step 5: Bromine Equivalents

Bromine most commonly forms a -1 ion, so its valence is 1. Therefore, \(2.0 \text{ moles} \times 1 = 2.0 \text{ equivalents}\).

Step 6: Cesium Equivalents

Cesium generally forms a +1 ion, resulting in a valence of 1. So, \(2.0 \text{ moles} \times 1 = 2.0 \text{ equivalents}\).

Step 7: Barium Equivalents

Barium usually forms a +2 ion, resulting in a valence of 2. Therefore, \(2.0 \text{ moles} \times 2 = 4.0 \text{ equivalents}\).

Key Concepts

Valence

Valence is a fundamental concept in chemistry that refers to the ability of an atom to bond with other atoms. It is directly linked to the atom's electron configuration and the number of electrons available to form bonds. When we talk about the valence of an ion, we're essentially referring to its charge.
For instance:

• Magnesium typically forms a +2 ion, meaning it can donate 2 electrons during chemical reactions, giving it a valence of 2.
• Aluminum usually forms a +3 ion, having 3 electrons available to donate, so its valence is 3.
• Sulfur can gain or share 2 electrons to reach the stable octet, resulting in a -2 valence.

Understanding valence helps in predicting how an element will react and what kind of compounds it can form.

Moles

The concept of moles is central in chemistry to quantify the amount of a substance. One mole corresponds to Avogadro's number, approximately \(6.022 \times 10^{23}\) particles, be they atoms, molecules, ions, etc.
Using moles allows chemists to work with the macroscopic amounts of substances easily, as it correlates chemical reactions to measurable quantities. In the context of "equivalents," the moles of an ion help determine its reactive capacity, especially as you multiply them by the valence of the ion to get the equivalent value, which expresses how many mole-equivalents are involved in a reaction.
For example, 2.0 moles of an ion multiplied by its valence provide a numerical figure used in stoichiometry calculations.

Ion Charges

Ion charges are integral to understanding how ions interact and bond in chemical reactions. The charge of an ion arises from the loss or gain of electrons. Ions with positive charges are called cations, while ions with negative charges are referred to as anions. The magnitude of the charge is crucial because:

• It determines the valence, showing how many charges are available to participate in chemical reactions.
• Dictates the strength and type of electrostatic forces the ion can exert on its surroundings.
• Plays a key role in determining the physical properties and reactivity of the compound formed.

For example, a magnesium ion has a +2 charge because it loses two electrons, and thus, it can form stable compounds by donating those electrons.

Reactive Capacity

Reactive capacity is a term often applied when understanding how much of a substance can participate in a given chemical reaction. It is a measure of a substance's potence or ability to engage in chemical transformations. In relation to equivalents, reactive capacity is calculated by multiplying the moles of a substance by its valence.

• A higher valence indicates greater reactive capacity, as more electrons can be transferred in reactions.
• It provides a simplified way of measuring how many reaction units an entity of a substance carries.

Thus, reactive capacity helps chemists and students predict how substances will behave in reactions, how they combine, and balance chemical equations accurately.