Problem 58 - General Chemistry: Principles and Modern Applications

Question

A \(7.55 \mathrm{g}\) sample of \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})\) is added to \(125 \mathrm{mL}\) of a vinegar that is \(0.762 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH} .\) Will the resulting solution still be acidic? Explain.

Step-by-Step Solution

Answer

No, the resulting solution will not be acidic. All of the acetic acid in the vinegar (\(\mathrm{CH}_{3} \mathrm{COOH}\)) will react with sodium carbonate (\(\mathrm{Na}_{2} \mathrm{CO}_{3}\)), thus neutralizing the solution.

Step 1: Convert mass of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to moles

Since the molar mass of sodium carbonate (\(\mathrm{Na}_{2} \mathrm{CO}_{3}\)) is approximately \(106 \mathrm{g/mol}\), use this conversion factor to convert the mass of the sodium carbonate to moles: \(\frac {7.55 g} {106 g/mol} = 0.0712 mol\).

Step 2: Determine the initial moles of \(\mathrm{CH}_{3} \mathrm{COOH}\)

You have \(0.762 M\) \(\mathrm{CH}_{3} \mathrm{COOH}\) in \(125 mL\) of solution. To find the initial moles, multiply the molarity by the volume in liters: \((0.762 M) * (0.125 L) = 0.0953 mol\).

Step 3: Determine the moles of \(\mathrm{CH}_{3} \mathrm{COOH}\) after reaction

When \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) reacts with \(\mathrm{CH}_{3} \mathrm{COOH}\), two moles of \(\mathrm{CH}_{3} \mathrm{COOH}\) are needed for each mole of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\). Therefore, the moles of \(\mathrm{CH}_{3} \mathrm{COOH}\) that react equals to \(2 * 0.0712 mol = 0.1424 mol\). After the reaction, the remaining moles of \(\mathrm{CH}_{3} \mathrm{COOH}\) is found by subtracting the initial moles of \(\mathrm{CH}_{3} \mathrm{COOH}\) by the moles that reacted: \(0.0953 mol - 0.1424 mol = -0.0471 mol\).

Step 4: Determine if the solution remains acidic

The amount of \(\mathrm{CH}_{3} \mathrm{COOH}\) after the reaction is negative, which implies that there is no \(\mathrm{CH}_{3} \mathrm{COOH}\) remaining and that all of it has reacted. Therefore, the solution will no longer be acidic.

Key Concepts

Sodium Carbonate

Sodium carbonate is a common chemical compound often found in household cleaning products. It is known by its chemical formula \( \mathrm{Na}_2\mathrm{CO}_3 \) and sometimes referred to as soda ash or washing soda.
Sodium carbonate is an alkaline substance, meaning it has a basic nature. It is commonly used to neutralize acids in various chemical reactions.
When sodium carbonate is added to an acidic solution, such as vinegar which contains acetic acid, a reaction occurs, producing carbon dioxide gas, water, and a salt.

• Sodium carbonate in reactions: acts as a base to neutralize acids.
• It releases carbon dioxide gas upon reacting with acids.
• Used in various industries for its cleaning and neutralizing properties.

Acetic Acid

Acetic acid is the key component of vinegar, giving it a distinctive sour taste and smell. Chemically, it is represented as \( \mathrm{CH}_3\mathrm{COOH} \). This compound is a weak organic acid, which means it does not completely dissociate into ions in water.
Acetic acid is widely used in cooking and cleaning, but it also plays an important role in various chemical reactions involving bases like sodium carbonate.

• Weak acid: only partially ionizes in solution.
• Reacts with bases to form salts and water, a typical acid-base neutralization reaction.
• Used as a preservative, solvent, and in the synthesis of chemical compounds.

This characteristic makes it valuable in industries from food to plastics, and as seen in reactions like with sodium carbonate, it plays critical roles in educational chemistry settings.

Molarity Calculation

Molarity is a measurement of concentration and is defined as moles of solute per liter of solution. It indicates how much of a substance is present in a given volume of liquid.
The calculation of molarity is crucial in preparing solutions and reacting them in the correct stoichiometric proportions.
You calculate molarity using the formula:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]

• This allows chemists to ensure they are using the right amounts for reactions.
• Eases the process of scaling reactions up or down depending on the desired output.
• Ensures that the reactants are in the necessary proportions to react completely without excess.

In the provided exercise, knowing the molarity of acetic acid helped determine the amount of substance present before the reaction commenced.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It allows us to predict how much of each substance is needed or produced in a chemical reaction.
This concept is rooted in the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.
In an acid-base reaction, stoichiometry helps determine how much of each reactant will interact. When sodium carbonate reacts with acetic acid, stoichiometry tells us exactly how many moles of acetic acid are required to completely react with the given amount of sodium carbonate.

• Uses balanced chemical equations to relate moles of reactants to moles of products.
• Ensures no excess reactants are wasted and that products are formed efficiently.
• Critical in predicting reaction outcomes and for industrial applications where yield and cost are significant.

This concept was pivotal in calculating the reaction's outcome, determining that all the acetic acid would be consumed, leaving a non-acidic solution.