Question

How many equivalents of an acid or base are in the following? (a) \(0.25 \mathrm{~mol} \mathrm{Mg}(\mathrm{OH})_{2}\) (b) \(2.5 \mathrm{~g} \mathrm{Mg}(\mathrm{OH})_{2}\) (c) \(15 \mathrm{~g} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

Short answer

(a) 0.5 equivalents; (b) 0.0858 equivalents; (c) 0.249 equivalents.

Step-by-step solution

Understanding Equivalents

The concept of equivalents is used to determine how many moles of reactive species (ions) are present. For bases like Mg(OH)₂, equivalents are based on the ability to provide OH⁻ ions. For acids like CH₃CO₂H, they are based on H⁺ ions.

Calculating Equivalents for Mg(OH)₂ in Moles

Since each molecule of Mg(OH)₂ can dissociate to provide 2 OH⁻ ions, 1 mole of Mg(OH)₂ represents 2 equivalents. Given 0.25 moles, calculate the equivalents as follows:\[\text{Equivalents} = 0.25 \text{ moles} \times 2 = 0.5 \text{ equivalents}\]

Converting Grams to Moles for Mg(OH)₂

First, find the molar mass of Mg(OH)₂: Mg = 24.31 g/mol, O = 16.00 g/mol, H = 1.01 g/mol. Thus, Mg(OH)₂ = 24.31 + 2(16.00 + 1.01) = 58.32 g/mol. Convert 2.5 grams to moles:\[\text{Moles} = \frac{2.5 \text{ g}}{58.32 \text{ g/mol}} \approx 0.0429 \text{ moles}\]

Calculating Equivalents for Mg(OH)₂ in Grams

Now, calculate the equivalents from the moles:\[\text{Equivalents} = 0.0429 \text{ moles} \times 2 \approx 0.0858 \text{ equivalents}\]

Converting Grams to Moles for CH₃CO₂H

First, find the molar mass of CH₃CO₂H: C = 12.01 g/mol, H = 1.01 g/mol, O = 16.00 g/mol. Thus, CH₃CO₂H = 2(12.01) + 4(1.01) + 2(16.00) = 60.05 g/mol. Convert 15 grams to moles:\[\text{Moles} = \frac{15 \text{ g}}{60.05 \text{ g/mol}} \approx 0.249 \text{ moles}\]

Calculating Equivalents for CH₃CO₂H

Since CH₃CO₂H can provide 1 H⁺ ion, 1 mole corresponds to 1 equivalent. Thus, the equivalents are:\[\text{Equivalents} = 0.249 \text{ moles} \times 1 = 0.249 \text{ equivalents}\]

Key concepts

Molar Mass Calculation

Understanding molar mass is a fundamental concept in chemistry. It is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, you need to sum up the atomic masses of each element present in the molecule.
For example, the molar mass of magnesium hydroxide, Mg(OH)₂, is calculated by adding the atomic masses of magnesium (Mg), oxygen (O), and hydrogen (H). Magnesium has an atomic mass of 24.31 g/mol, oxygen is 16.00 g/mol, and hydrogen is 1.01 g/mol. Therefore, the molar mass of Mg(OH)₂ is 58.32 g/mol, determined as follows: 24.31 + 2(16.00 + 1.01).
Another example is acetic acid, CH₃CO₂H, with a molar mass of 60.05 g/mol, calculated by summing: 2 carbon atoms (2 x 12.01 g/mol), 4 hydrogen atoms (4 x 1.01 g/mol), and 2 oxygen atoms (2 x 16.00 g/mol).

• Step 1: Identify the elements present in the molecule.
• Step 2: Find the atomic mass of each element.
• Step 3: Multiply the atomic mass of each element by the number of times it appears in the compound.
• Step 4: Add the masses for the final molar mass of the compound.

Proper molar mass calculation is critical for further chemical calculations, such as converting between grams and moles.

Acid-Base Chemistry

Acid-base chemistry is an important area that deals with the behavior of acids and bases in various chemical processes. An acid is a substance that can donate hydrogen ions (H⁺), while a base can accept hydrogen ions or provide hydroxide ions (OH⁻).
Understanding the concept of equivalents is crucial in acid-base reactions. Equivalents measure the reactive capacity of acids and bases. For example, magnesium hydroxide (Mg(OH)₂) is a base that can donate two OH⁻ ions per molecule, meaning each mole of Mg(OH)₂ has two equivalents. Similarly, acetic acid (CH₃CO₂H) can donate one H⁺ ion per molecule, therefore one mole corresponds to one equivalent.
Equivalents allow chemists to predict the outcomes of acid-base reactions more accurately by normalizing the different reactive capacities of the compounds involved.

• Step 1: Identify whether the substance is an acid or a base.
• Step 2: Determine how many H⁺ or OH⁻ ions the compound can donate or accept.
• Step 3: Calculate the equivalents based on moles of reactive species present.

This understanding is essential for balancing chemical equations and predicting the extent of reactions.

Chemical Stoichiometry

Chemical stoichiometry involves using balanced chemical equations to determine the relationships between the amounts of reactants and products. It is fundamental in calculating how much of a substance is needed or produced in a reaction.
Stoichiometry relies on the law of conservation of mass, meaning all atoms in the reactants must appear in the products. To solve stoichiometric problems, we use ratios from the balanced equation, molar masses, and the concept of moles.
In the context of equivalents, stoichiometry plays a role in understanding how different amounts of acids and bases interact. For Mg(OH)₂ and CH₃CO₂H, equivalents allow conversion between different forms to find out how much base is needed to neutralize a given acid, and vice versa.

• Step 1: Write and balance the chemical equation.
• Step 2: Convert masses to moles using molar mass if necessary.
• Step 3: Utilize mole ratios from the balanced equation for conversions.
• Step 4: Calculate desired quantities using stoichiometric relationships.

Mastery of stoichiometry ensures proper calculation of reactant and product amounts, making it indispensable for researching and performing chemical reactions.