Question

The fizz produced when an Alka-Seltzer tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) :\) $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) & \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment 1.00 g of sodium bicarbonate and 1.00 g of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?

Short answer

(a) The limiting reactant is sodium bicarbonate (NaHCO3). (b) 0.524 grams of carbon dioxide (CO2) are produced. (c) 0.236 grams of citric acid (H3C6H5O7) remain after the reaction.

Step-by-step solution

Calculate the moles of each reactant

We are given 1.00 g of sodium bicarbonate (NaHCO3) and 1.00 g of citric acid (H3C6H5O7). First, we must find the molar mass of each reactant: The molar mass of NaHCO3: \(Na: 22.99 g/mol\), \(H: 1.01 g/mol\), \(C: 12.01 g/mol\), and \(O: 16.00 g/mol\) Molar mass of NaHCO3 = 22.99 + 1.01 + 12.01 + (3 × 16.00) = 84.01 g/mol The molar mass of H3C6H5O7: \(H: 1.01 g/mol\), \(C: 12.01 g/mol\), and \(O: 16.00 g/mol\) Molar mass of H3C6H5O7 = (3 × 1.01) + (6 × 12.01) + (5 × 1.01) + (7 × 16.00) = 192.12 g/mol Now we'll calculate moles of each reactant. Moles of NaHCO3 = 1.00 g / 84.01 g/mol = 0.0119 mol Moles of H3C6H5O7 = 1.00 g / 192.12 g/mol = 0.00520 mol

Determine the limiting reactant

Using the balanced chemical equation, we can determine that 3 moles of NaHCO3 react with 1 mole of H3C6H5O7: \(3NaHCO_3 + H_3C_6H_5O_7 → 3CO_2 + 3H_2O + Na_3C_6H_5O_7\) Divide the moles of each reactant by their corresponding stoichiometric coefficient: NaHCO3: 0.0119 mol / 3 = 0.00397 mol H3C6H5O7: 0.00520 mol / 1 = 0.00520 mol The reactant with the smallest result is the limiting reactant. Therefore, NaHCO3 is the limiting reactant.

Calculate the mass of carbon dioxide produced

Using stoichiometry, determine the amount of carbon dioxide produced from the limiting reactant (NaHCO3). From the balanced chemical equation, we see that 3 moles of NaHCO3 produce 3 moles of CO2. So, the ratio of produced CO2 to the used NaHCO3 is 1:1. Moles of CO2 produced = 0.0119 mol Now, find the molar mass of CO2: Molar mass of CO2 = 12.01 + (2 × 16.00) = 44.01 g/mol Mass of CO2 produced = (0.0119 mol) × (44.01 g/mol) = 0.524 g

Calculate the mass of the excess reactant remaining

Now we have to determine the amount of H3C6H5O7 that reacted with the limiting reactant (NaHCO3). Moles of H3C6H5O7 reacted = 0.0119 mol (NaHCO3) × (1 mol H3C6H5O7 / 3 mol NaHCO3) = 0.00397 mol Moles of H3C6H5O7 remaining = Initial moles of H3C6H5O7 - Moles of H3C6H5O7 reacted = 0.00520 mol - 0.00397 mol = 0.00123 mol Mass of H3C6H5O7 remaining = (0.00123 mol) × (192.12 g/mol) = 0.236 g Answer: (a) The limiting reactant is sodium bicarbonate (NaHCO3). (b) 0.524 grams of carbon dioxide (CO2) are produced. (c) 0.236 grams of citric acid (H3C6H5O7) remain after the reaction.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantifiable relationships between the reactants and products in a chemical reaction. It's based on the conservation of mass where the total mass of reactants equals the total mass of products.

In the context of the Alka-Seltzer reaction, stoichiometry allows us to predict the amounts of products formed and the reactants needed for the reaction. By converting grams to moles, we establish a comparable measure across different substances. The balanced chemical equation provides the mole ratio of reactants to products, which is crucial for identifying the limiting reactant and determining the amounts of products formed.

In this scenario, stoichiometry guides us through calculating moles from grams, using molar masses, and applying the mole ratios from the balanced equation to find out which reactant will run out first (the limiting reactant) and how much of the other reactants will remain (the excess reactant).

Mole Concept

The mole concept is foundational to understanding stoichiometry. It is the unit of amount in chemistry and provides a way of counting atoms, molecules, or formula units by weighing them. One mole corresponds to Avogadro's number, which is approximately 6.022 x 10²³ entities.

When working with the Alka-Seltzer experiment, we first determine how many moles of each reactant we have by dividing their weight by their respective molar masses. This step is crucial because reactions happen on a molecular level, and the mole allows us to use mass as a bridge to count molecules indirectly.

In the example given, converting the grams to moles is the first step in finding the limiting reactant. Understanding the mole concept is essential for this conversion and for interpreting the mole ratios provided by the balanced chemical equation.

Chemical Reaction

A chemical reaction involves the conversion of one set of chemical substances (reactants) to another (products). Reactions are governed by the laws of conservation of mass and balanced by stoichiometric coefficients that ensure that the number of atoms for each element is the same on both sides of the equation.

The fizz when an Alka-Seltzer tablet reacts with water is the visible result of such a chemical reaction. Specifically, it's a type of acid-base reaction where sodium bicarbonate and citric acid react to form carbon dioxide gas, water, and sodium citrate.

The balanced chemical equation of the reaction informs us about the stoichiometry—the exact proportions of reactants necessary for the reaction to proceed without any remainder. It's essentially a recipe that chemists use to predict the outcome of a reaction under ideal conditions. Using these coefficients, we can determine which reactant will be used up first and become the limiting reactant, thus controlling the extent of the reaction and the amount of product formed.