Problem 107 - Chemistry and Chemical Reactivity

Question

On General ChemistryNow CD-ROM or website Screen 4.12, Chemical Puzzler, you can explore the reaction of baking soda (NaHCO \(_{3}\) ) with the acetic acid in vinegar. Suppose you place exactly 200 mL. of vinegar in the beaker and add baking soda. The reaction occurring is \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{NaHCO}_{3}(\mathrm{aq}) \longrightarrow\) $$\mathrm{NaCH}_{3} \mathrm{CO}_{2}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)$$ How many spoonfuls of baking soda is required to consume the acetic acid in the \(200-\mathrm{mL}\). sample? (Assume there is \(50.0 \mathrm{g}\) of acetic acid per liter of vinegar and a spoonful of baking soda has a mass of \(3.8 \mathrm{g} .\) ) Are three spoonfuls sufficient? Are four spoonfuls enough?

Step-by-Step Solution

Answer

Three spoonfuls are insufficient; four spoonfuls are enough.

Step 1: Calculate the mass of acetic acid in the sample

Given that there is 50.0 g of acetic acid per liter of vinegar, we need to adjust this for our 200 mL sample. Since 200 mL is 0.2 L, the mass of acetic acid in the sample is calculated as follows:\[ \text{Mass of acetic acid} = 50.0 \text{ g/L} \times 0.2 \text{ L} = 10.0 \text{ g} \]

Step 2: Determine moles of acetic acid

Now calculate the moles of acetic acid using its molar mass. The molar mass of acetic acid (\(\mathrm{CH}_3\mathrm{CO}_2\mathrm{H}\)) is approximately 60.05 g/mol. Thus, the moles of acetic acid are:\[ \text{Moles of acetic acid} = \frac{10.0 \text{ g}}{60.05 \text{ g/mol}} \approx 0.1665 \text{ moles} \]

Step 3: Calculate moles of baking soda needed

From the balanced chemical equation, the reaction between acetic acid and baking soda (\(\mathrm{NaHCO}_3\)) occurs in a 1:1 molar ratio. Therefore, 0.1665 moles of baking soda are required. The molar mass of NaHCO\(_3\) is approximately 84.01 g/mol, so we calculate the mass needed:\[ \text{Mass of baking soda} = 0.1665 \text{ moles} \times 84.01 \text{ g/mol} \approx 14.00 \text{ g} \]

Step 4: Determine the number of spoonfuls required

Each spoonful of baking soda weighs 3.8 g. Therefore, the number of spoonfuls required can be calculated:\[ \text{Number of spoonfuls} = \frac{14.00 \text{ g}}{3.8 \text{ g/spoonful}} \approx 3.68 \text{ spoonfuls} \]

Step 5: Evaluate spoonful sufficiency

Since 3.68 spoonfuls are required, three spoonfuls are not sufficient. Thus, at least four spoonfuls are needed to consume all the acetic acid in the vinegar.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry dealing with the quantitative relationships between reactants and products in a chemical reaction. It helps us know the exact amount of substances needed for a reaction to occur without any leftover reactants. Let's break it down. In our example, we have a reaction between baking soda (NaHCO₃) and acetic acid (CH₃CO₂H) found in vinegar.

• This reaction is represented by a balanced chemical equation, which tells us the ratio in which the chemicals react. In this case, it's a 1:1 ratio, meaning one mole of baking soda reacts with one mole of acetic acid.
• Using stoichiometry, we can determine how much baking soda is necessary to completely react with the acetic acid in a given volume of vinegar.
• First, we find out how much acetic acid there is in our sample of vinegar and convert it to moles.
• Then, using the 1:1 ratio from the balanced equation, we know we need the same number of moles of baking soda to react with all of the acetic acid.

In our specific problem, this led us to calculate that 3.68 spoonfuls of baking soda are needed. Knowing stoichiometry allows us to perform similar calculations for a variety of reactions, ensuring accurate chemical use and preventing waste.

Acid-Base Reactions

Acid-base reactions are a common type of chemical reaction where an acid reacts with a base to produce water and a salt. These are also known as neutralization reactions. In the case of our scenario, acetic acid (CH₃CO₂H) acts as the acid, and baking soda (NaHCO₃) functions as the base. When they react, the products formed are sodium acetate (NaCH₃CO₂), carbon dioxide (CO₂), and water (H₂O).

• The general formula for an acid-base reaction is: \[\text{acid} + \text{base} \rightarrow \text{salt} + \text{water}\]In this reaction, the CO₂ gas is a notable product because it is released as bubbles, which are visible when vinegar and baking soda are mixed.
• Acid-base reactions are not only fascinating but also practically important as they are widely used in cooking, cleaning, and other everyday applications.

Understanding the basics of acid-base reactions helps in identifying the outcomes when acids and bases come in contact, explaining visible changes and ensuring the right amount of reactants are used.

Molar Mass

Molar mass is a critical concept in chemistry that refers to the mass of one mole of a given substance, expressed in grams per mole (g/mol). It helps convert between mass and moles, which is essential for stoichiometry calculations.

• In our example, we calculate the molar mass of acetic acid (CH₃CO₂H) and baking soda (NaHCO₃).
• The molar mass is found by summing the weights of all atoms in a molecule. For acetic acid, the molar mass is approximately 60.05 g/mol, while for baking soda, it’s about 84.01 g/mol.
• Knowing the molar mass allows us to convert the given mass of a compound into moles, making it possible to use stoichiometry correctly.

Molar mass links the microscopic chemical world with the macroscopic world of grams and liters, making it possible to measure chemicals precisely for reactions. Understanding and using molar mass is vital for any chemist and helps with accurate experimental results.