Question

Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: \(3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) \longrightarrow\) $$ 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) $$ a. What mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used for every \(1.0 \times 10^{2} \mathrm{mg}\) \(\mathrm{NaHCO}_{3} ?\) b. What mass of \(\mathrm{CO}_{2}(g)\) could be produced from such a mixture?

Short answer

a. For every \(1.0 \times 10^{2} \mathrm{mg}\) \(\mathrm{NaHCO}_{3}\), approximately \(0.0229 \mathrm{g}\) of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used. b. From such a mixture, approximately \(0.00526 \mathrm{g}\) of \(\mathrm{CO}_{2}(g)\) could be produced.

Step-by-step solution

Calculate moles of Sodium Bicarbonate, NaHCO3

First, we need to convert the given mass of Sodium Bicarbonate, NaHCO3, into moles. To do this, use the molar mass of NaHCO3 (84.01 g/mol). The given mass is in mg, so we will convert it to grams: \( 1.0 \times 10^2 mg = 0.10 g \) Now we can find the moles of NaHCO3: moles of NaHCO3 = \(\frac{0.10 \mathrm{g}}{84.01 \mathrm{g/mol}}\)

Determine moles of Citric Acid, C6H8O7

Using the stoichiometry of the balanced chemical equation, we can find the moles of Citric Acid, C6H8O7, needed: \( 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q)\longrightarrow\) From the balanced equation, we can see that for every three moles of NaHCO3, one mole of C6H8O7 is needed. We can set up a proportional relationship: \(\frac{\text{moles of C6H8O7}}{1} = \frac{\text{moles of NaHCO3}}{3}\) Now, solve for moles of C6H8O7.

Convert moles of Citric Acid to mass

Now that we have found the moles of C6H8O7 needed, we can convert it back to mass using the molar mass of C6H8O7 (192.12 g/mol): mass of C6H8O7 = moles of C6H8O7 × (192.12 g/mol)

Calculate moles and mass of CO2 produced

Using the stoichiometry of the balanced chemical equation, we can find the moles of CO2 produced. For every three moles of NaHCO3, three moles of CO2 are produced. Therefore, the moles of CO2 produced would be the same as the moles of NaHCO3. moles of CO2 = moles of NaHCO3 Now, convert the moles of CO2 to mass using the molar mass of CO2 (44.01 g/mol): mass of CO2 = moles of CO2 × (44.01 g/mol) Now you have both the mass of Citric Acid needed for every 100 mg NaHCO3 and the mass of CO2 that can be produced from this mixture.

Key concepts

Chemical Equations

Chemical equations are a shorthand way of representing chemical reactions. They use symbols and formulas for the elements and compounds involved, and evenly balance both reactants and products.
For example, in the reaction \[3 \text{NaHCO}_3(aq) + \text{C}_6 \text{H}_8 \text{O}_7(aq) \rightarrow 3 \text{CO}_2(g) + 3 \text{H}_2 \text{O}(l) + \text{Na}_3 \text{C}_6 \text{H}_5 \text{O}_7(aq)\], the equation represents the interaction between Sodium Bicarbonate and Citric Acid.
This reaction produces carbon dioxide, water, and a sodium citrate compound.

• The coefficients (numbers in front of the formulas) tell us the proportion of molecules or moles necessary to balance the reaction.
• In this case, 3 moles of NaHCO3 react with 1 mole of citric acid to produce 3 moles of carbon dioxide.

Understanding how to balance chemical equations is essential for predicting how much product will be formed in a reaction.

Molar Mass

The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is critical for converting between mass and moles in chemical calculations.
To use molar mass for conversions, simply multiply or divide the amount of substance (in grams or moles) by the molar mass.

• Sodium Bicarbonate (NaHCO3) has a molar mass of 84.01 g/mol. This means that 84.01 grams of NaHCO3 contain one mole of this substance.
• Citric Acid (C6H8O7) has a molar mass of 192.12 g/mol.
• These values allow us to convert a given mass to the number of moles, which are essential for reaction stoichiometry.

Accurate use of molar mass bridges the gap between what we weigh and the number of molecules or moles present.

Sodium Bicarbonate (NaHCO3)

Sodium Bicarbonate, commonly known as baking soda, is a white solid crystalline compound. It is widely used in baking, cleaning, and in medicinal preparations like antacids.
When it reacts with acids, like citric acid, it releases carbon dioxide gas, which is the source of the "fizz."

• In the reaction equation presented, it acts as both a reactant and a source of CO2 production.
• It plays a critical role in maintaining the stoichiometric balance in the reaction with citric acid.

Understanding its molar mass and reaction properties is crucial for predicting the outputs in practical experiments, such as the fizz produced in effervescent tablets.

Citric Acid (C6H8O7)

Citric Acid is a weak organic acid known for its sour taste and presence in citrus fruits like lemons and oranges. It is often used as a flavoring and preservative in food and beverages.
In chemical reactions, its properties allow it to react with bases like sodium bicarbonate to produce desired outputs like carbon dioxide.

• The balanced chemical equation shows that 1 mole of citric acid reacts with 3 moles of sodium bicarbonate.
• Its molar mass of 192.12 g/mol is used to calculate the mass required for any given reaction based on stoichiometry.
• The reaction not only releases CO2 but also forms sodium citrate, an important compound in biochemistry.

Grasping its role in reactions helps in understanding its applications and reaction dynamics in various fields, from cooking to pharmaceuticals.