Question

Calculate the mass needed for each of the following ion equivalents: (a) \(0.25 \mathrm{Eq} \mathrm{Ca}^{2+}\) (b) \(75 \mathrm{mEq} \mathrm{K}^{+}\) (c) \(199 \mathrm{mEg} \mathrm{SO}_{4}^{2-}\) (d) \(0.65 \mathrm{Eq} \mathrm{PO}_{4}^{3-}\)

Short answer

(a) 5.01 g Ca, (b) 2.93 g K, (c) 9.56 g SO₄, (d) 20.58 g PO₄.

Step-by-step solution

Understanding Ion Equivalents

Ion equivalents refer to the amount of a substance that reacts with or supplies one mole of hydrogen ions (H⁺) in a chemical reaction. The equivalent weight is calculated as the molar mass divided by the valence (charge).

Calculate Mass for Ca²⁺

Calcium (Ca) with a charge of +2 has an atomic mass of approximately 40.08 g/mol. The equivalent weight of Ca²⁺ is given by:\[ \text{Equivalent weight of Ca}^{2+} = \frac{40.08 \text{ g/mol}}{2} = 20.04 \text{ g/Eq} \]The mass for 0.25 Eq is:\[ 0.25 \times 20.04 = 5.01 \text{ g} \]

Calculate Mass for K⁺

Potassium (K) with a charge of +1 has an atomic mass of approximately 39.10 g/mol. The equivalent weight of K⁺ is the same as its atomic mass (39.10 g/Eq).The mass for 75 mEq is given by converting mEq to Eq:\[ 75 \text{ mEq} = 0.075 \text{ Eq} \]\[ 0.075 \times 39.10 = 2.93 \text{ g} \]

Calculate Mass for SO₄²⁻

Sulfate (SO₄²⁻) has a molecular mass of about 96.06 g/mol. The equivalent weight of SO₄²⁻ is:\[ \text{Equivalent weight of SO}_4^{2-} = \frac{96.06 \text{ g/mol}}{2} = 48.03 \text{ g/Eq} \]The mass for 199 mEq is:\[ 199 \text{ mEq} = 0.199 \text{ Eq} \]\[ 0.199 \times 48.03 = 9.56 \text{ g} \]

Calculate Mass for PO₄³⁻

Phosphate (PO₄³⁻) has a molecular mass of about 94.97 g/mol. The equivalent weight of PO₄³⁻ is:\[ \text{Equivalent weight of PO}_4^{3-} = \frac{94.97 \text{ g/mol}}{3} = 31.66 \text{ g/Eq} \]The mass for 0.65 Eq is:\[ 0.65 \times 31.66 = 20.58 \text{ g} \]

Key concepts

Molar Mass Calculations

Understanding molar mass is a foundational concept in chemistry. Molar mass is essentially the total mass of one mole of a given substance. We express this in grams per mole (g/mol). Molar mass helps us quantify the amount of substance based on its atomic or molecular characteristics. To find the molar mass, simply sum up the atomic masses of all atoms in the chemical formula. For example:

• Calcium (Ca): Atomic mass = 40.08 g/mol (since it is a single element, this is the molar mass)


• Sulfate (SO₄): Total molecular mass = (S = 32.07 + 4 × O = 16.00 × 4) = 96.06 g/mol

Molar mass is crucial in chemical calculations because it relates moles to grams, allowing us to measure substances conveniently.

Chemical Reactions

Chemical reactions are processes where reactants transform into products. They follow the conservation of mass, meaning no atoms are lost or gained; they simply rearrange. Understanding chemical reactions involves knowing:

• Reactants: Substances present before the chemical change.


• Products: New substances formed from the reaction.
• Balancing equations to ensure equal numbers of atoms for each element on both sides.

Reaction examples often showcase the role of ion equivalents. For instance, in acid-base reactions, equivalents measure the amount of acid or base reacting. This concept is extremely useful when dealing with compounds that dissociate into ions, like acids and bases.

Valence Charge

Valence charge refers to the charge an atom holds after forming compounds by gaining or losing electrons. This charge plays a key role in understanding how atoms bond and interact. For ions, the valence charge is the charge an atom has when it's an ion. For example:

• Calcium ion (\( \text{Ca}^{2+} \)): Has lost two electrons, so the charge is +2.


• Phosphate (\( \text{PO}_4^{3-} \)): Carries a -3 charge, indicating 3 extra electrons.

Valence charges determine how ions will combine in chemical reactions, forming electrically neutral compounds. They also influence the calculation of equivalent weight, as equivalent weight is determined by dividing the molar mass by the ion's valence.

Equivalent Weight

Equivalent weight is an important concept in chemistry, especially when dealing with reactions involving ions. It is defined as the mass of a substance which will combine with or displace one mole of hydrogen ions (H⁺) in a chemical reaction. To calculate equivalent weight, you need:

• Molar Mass: The total mass of one mole of the substance.


• Valence: The charge of the ion or the number of electrons involved in the reaction.

The formula for calculating equivalent weight is:\[\text{Equivalent Weight} = \frac{\text{Molar Mass}}{\text{Valence}}\]For practical use, knowing the equivalent weight helps in converting between moles and equivalents, especially in titrations or stoichiometry. For instance, the equivalent weight of calcium (\( \text{Ca}^{2+} \)) with a molar mass of 40.08 g/mol and a charge of +2 is 20.04 g/Eq. This means 20.04 grams of calcium will supply or react with one mole of hydrogen ions.