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 \(1.00 \mathrm{~g}\) of sodium bicarbonate and \(1.00 \mathrm{~g}\) 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) Sodium bicarbonate (NaHCO3) is the limiting reactant. (b) 0.524 g of carbon dioxide (CO2) is formed. (c) 0.230 g of the excess reactant, citric acid (H3C6H5O7), remains after the reaction.

Step-by-step solution

Calculate the number of moles of reactants.

To determine the limiting reactant and calculate the mass of product formed, we first need to find the number of moles of each reactant present. We can find this using their given masses and molar masses. For sodium bicarbonate, NaHCO3: \(Molar~mass~of~NaHCO3 = 22.99 + 1.01 + 12.01 + 3(16.00) = 84.01~g/mol \) Number of moles of NaHCO3: \(n_{NaHCO3} = \frac{mass_{NaHCO3}}{molar~mass_{NaHCO3}} = \frac{1.00~g}{84.01~g/mol} = 0.0119~mol \) For citric acid, H3C6H5O7: \(Molar~mass~of~H3C6H5O7 = 3(1.01) + 6(12.01) + 5(1.01) + 7(16.00) = 192.12~g/mol \) Number of moles of H3C6H5O7: \(n_{H3C6H5O7} = \frac{mass_{H3C6H5O7}}{molar~mass_{H3C6H5O7}} = \frac{1.00~g}{192.12~g/mol} = 0.0052~mol \)

Determine the limiting reactant.

Now we need to find which reactant is the limiting reactant. The balanced equation tell us that 3 moles of NaHCO3 are required to react with 1 mole of H3C6H5O7. So, we will find the mole ratio of NaHCO3 to H3C6H5O7 and compare it to this stoichiometric ratio: \(Mole~ratio = \frac{n_{NaHCO3}}{n_{H3C6H5O7}} = \frac{0.0119~mol}{0.0052~mol} = 2.29 \) Since the required mole ratio is 3:1 and we have a mole ratio less than that (2.29), this indicates that NaHCO3 is the limiting reactant.

Calculate the mass of carbon dioxide formed.

Now that we know the limiting reactant, we can calculate the amount of carbon dioxide formed. The balanced equation tells us that 3 moles of NaHCO3 produce 3 moles of CO2. Number of moles of CO2 formed: \(n_{CO2} = n_{NaHCO3} = 0.0119~mol \) To find the mass of CO2 formed, we'll multiply the moles of CO2 by its molar mass: \(Molar~mass~of~CO2 = 12.01 + 2(16.00) = 44.01~g/mol \) Mass of CO2 formed: \(mass_{CO2} = n_{CO2} × molar~mass_{CO2} = 0.0119~mol × 44.01~g/mol = 0.524~g \)

Calculate the mass of the excess reactant remaining.

Lastly, we need to determine the mass of the unreacted H3C6H5O7. We'll first find out how many moles of it reacted with NaHCO3 by using the stoichiometry in the balanced equation (3 moles of NaHCO3 react with 1 mole of H3C6H5O7): Moles of H3C6H5O7 reacted: \(n_{H3C6H5O7~reacted} = \frac{n_{NaHCO3}}{3} = \frac{0.0119~mol}{3} = 0.0040~mol \) Next, we'll subtract the moles of H3C6H5O7 that reacted from the initial number of moles: Moles of H3C6H5O7 remaining: \(n_{H3C6H5O7~remaining} = n_{H3C6H5O7} - n_{H3C6H5O7~reacted} = 0.0052~mol - 0.0040~mol = 0.0012~mol \) Finally, we'll convert the moles of H3C6H5O7 remaining to mass: Mass of H3C6H5O7 remaining: \(mass_{H3C6H5O7~remaining} = n_{H3C6H5O7~remaining} × molar~mass_{H3C6H5O7} = 0.0012~mol × 192.12~g/mol = 0.230~g \) To summarize our results: (a) The limiting reactant is sodium bicarbonate (NaHCO3). (b) The mass of carbon dioxide (CO2) formed is 0.524 g. (c) The mass of the excess reactant, citric acid (H3C6H5O7), remaining is 0.230 g.

Key concepts

Stoichiometry

Stoichiometry is like a recipe for chemistry. It's the part of chemistry that tells us how to mix ingredients together to make a product. Just like when you need a certain amount of flour and sugar to make cookies, you need a certain amount of chemicals to make a reaction happen. Stoichiometry uses the mole concept, which is like a counting unit for atoms and molecules, allowing chemists to figure out how much of each reactant they need and how much product they will get in return.

In the case of the Alka-Seltzer reaction, stoichiometry helps us to understand the precise amounts of sodium bicarbonate and citric acid that are needed to react completely without leaving leftovers. It's a balancing act, just like making sure you have just enough chairs for guests at a party — not too many and not too few. Through the calculation steps outlined in the exercise, we've used stoichiometry to solve practical questions such as which reactant will run out first (the limiting reactant) and how much of each substance we'll end up with at the end of the reaction.

Mole Concept

The mole concept is a fundamental idea in chemistry that relates the mass of substances to the number of particles. One mole equals Avogadro's number of particles (atoms, molecules, ions, etc.), which is approximately 6.022 x 10²³. The term 'mole' is to chemists what 'dozen' is to bakers—except instead of twelve, it's a very, very large number.

Understanding the mole concept is crucial when we calculate the number of moles of reactants in our Alka-Seltzer experiment. We determine the number of moles by dividing the mass of the reactant by its molar mass. This process allows us to compare amounts of different substances in a meaningful way, guiding us towards discovering the limiting reactant. To improve students' understanding of the mole concept, we could provide visual aids that represent the scale of a mole, as the number is too large to easily visualize.

Chemical Reactions

A chemical reaction is a process where some substances, called reactants, change into different substances, called products. These transformations occur when atoms and molecules rearrange themselves in new ways. The Alka-Seltzer reaction is a great example – you start with sodium bicarbonate and citric acid, and end up with carbon dioxide, water, and a salt compound.

Understanding chemical reactions involves knowing how reactants combine and what they form. The balanced equation in our Alka-Seltzer example gives us a map of the reaction: for every three units of sodium bicarbonate, we need one unit of citric acid to get the desired products. When one reactant runs out, the reaction stops, which is why the concept of the limiting reactant is so important. Enhancing the exercise's educational value could involve showing real-life demonstrations or simulations of the reaction, providing students with a more concrete grasp of the process.