Problem 104 - Chemistry and Chemical Reactivity

Question

An Alka-Seltzer tablet contains exactly \(100 .\) mg of citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7},\) plus some sodium bicarbonate. What mass of sodium bicarbonate is required to consume \(100 .\) mg of citric acid by the following reaction? \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})+3 \mathrm{NaHCO}_{3}(\mathrm{aq}) \rightarrow\) $$ 3 \mathrm{H}_{2} \mathrm{O}(\ell)+3 \mathrm{CO}_{2}(\mathrm{g})+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) $$

Step-by-Step Solution

Answer

131 mg of sodium bicarbonate is required.

Step 1: Determine the Molar Mass of Citric Acid and Sodium Bicarbonate

First, we need to determine the molar mass of citric acid (\( H_3C_6H_5O_7 \)) and sodium bicarbonate (\( NaHCO_3 \)).- **Citric Acid**: - Carbon (C): \(12.01 \, g/mol \times 6 = 72.06 \, g/mol\) - Hydrogen (H): \(1.01 \, g/mol \times 8 = 8.08 \, g/mol\) - Oxygen (O): \(16.00 \, g/mol \times 7 = 112.00 \, g/mol\) - Total: \(72.06 + 8.08 + 112.00 = 192.14 \, g/mol\)- **Sodium Bicarbonate**: - Sodium (Na): \(22.99 \, g/mol\) - Hydrogen (H): \(1.01 \, g/mol\) - Carbon (C): \(12.01 \, g/mol\) - Oxygen (O): \(16.00 \, g/mol \times 3 = 48.00 \, g/mol\) - Total: \(22.99 + 1.01 + 12.01 + 48.00 = 84.01 \, g/mol\)

Step 2: Calculate the Moles of Citric Acid

Using the molar mass of citric acid, calculate the number of moles in \(100 \, mg\) (which is \(0.1 \, g\)). \[\text{Moles of Citric Acid} = \frac{0.1 \, g}{192.14 \, g/mol} \approx 0.00052 \, mol\]

Step 3: Use Stoichiometry to Find Moles of Sodium Bicarbonate

From the balanced chemical equation, we can see that 1 mole of citric acid reacts with 3 moles of sodium bicarbonate. \[\text{Moles of } NaHCO_3 = 0.00052 \, mol \times 3 = 0.00156 \, mol\]

Step 4: Calculate the Mass of Sodium Bicarbonate Required

Now, convert the moles of sodium bicarbonate to mass using its molar mass.\[\text{Mass of } NaHCO_3 = 0.00156 \, mol \times 84.01 \, g/mol \approx 0.131 g \]This is equivalent to \(131 \, mg\) of sodium bicarbonate.

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry, allowing us to convert between the mass of a substance and the amount in moles, facilitating stoichiometric calculations in chemical reactions. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
To calculate the molar mass, add up the atomic masses of all the atoms in a molecule. For instance, consider citric acid, which has the molecular formula \(H_3C_6H_5O_7\). Each element in the compound contributes a specific number of atoms and thus a certain mass to the total.

• Carbon (C): 6 atoms × 12.01 g/mol = 72.06 g/mol
• Hydrogen (H): 8 atoms × 1.01 g/mol = 8.08 g/mol
• Oxygen (O): 7 atoms × 16.00 g/mol = 112.00 g/mol

Adding these together, the molar mass of citric acid is 192.14 g/mol. Similarly, for sodium bicarbonate (\(NaHCO_3\)), the molar mass is calculated as:

• Sodium (Na): 22.99 g/mol
• Hydrogen (H): 1.01 g/mol
• Carbon (C): 12.01 g/mol
• Oxygen (O): 3 atoms × 16.00 g/mol = 48.00 g/mol

Totaling these gives a molar mass of 84.01 g/mol. Knowing these values is crucial for converting between mass and moles, a key step in stoichiometry.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relationships between the quantities of reactants and products in chemical reactions. It allows chemists to predict how much product can be formed from a given amount of reactants or how much reactant is needed to form a desired amount of product.
To apply stoichiometry effectively, one must first have a balanced chemical equation, which shows the proportion in which reactants combine and products form. In the given reaction:
\[\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq) + 3 \mathrm{NaHCO}_{3}(aq) \rightarrow 3 \mathrm{H}_{2} \mathrm{O}(l) + 3 \mathrm{CO}_{2}(g) + \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(aq)\]
The coefficients indicate that 1 mole of citric acid reacts with 3 moles of sodium bicarbonate.
By converting the given quantity of citric acid (in moles) using its molar mass, we can apply these coefficients to find that it requires three times as many moles of sodium bicarbonate.
If 0.00052 moles of citric acid is present, multiplying by 3 (using stoichiometric coefficients) tells us that 0.00156 moles of sodium bicarbonate is needed. This relationship between reactants is determined by their molecular proportions as shown in the balanced equation.

Citric Acid

Citric acid is a weak organic acid with the chemical formula \(H_3C_6H_5O_7\). It naturally occurs in citrus fruits and is commonly used as a preservative and flavoring agent. In Alka-Seltzer tablets, it plays an active role in the reaction with sodium bicarbonate to produce carbon dioxide, which helps relieve conditions like heartburn.
The molecule consists of three carboxyl groups, making it triprotic, meaning it can donate three protons in a reaction. This property is what enables it to react readily with bases such as sodium bicarbonate in a neutralization reaction, where it effectively donates protons and is converted to its salt form.
When citric acid reacts with sodium bicarbonate, it produces water, carbon dioxide (which forms bubbles), and sodium citrate. This reaction not only aids in digestion but is also a fun practical demonstration of an acid-base reaction.

Sodium Bicarbonate

Sodium bicarbonate, commonly known as baking soda, is a chemical compound with the formula \(NaHCO_3\). It's a mild base used in baking, to neutralize acids, and in medicinal preparations such as antacids. In the context of Alka-Seltzer, its primary purpose is to react with acids like citric acid to produce carbon dioxide gas.
This reaction increases pressure in liquids, contributing to the effervescence or fizzing effect that is characteristic of Alka-Seltzer. The balanced chemical equation shows that in the reaction:

• One mole of citric acid reacts with three moles of sodium bicarbonate.
• This results in the formation of three moles of water and three moles of carbon dioxide gas, along with sodium citrate in solution.

Understanding the role of sodium bicarbonate in these reactions helps explain its multifaceted uses in both homes and industries. It provides the dual benefits of acid neutralization and gas production, making it an essential ingredient in various applications.