Question

Common soap is made by reacting sodium carbonate with stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH}\). Write a balanced equation for the reaction.

Short answer

The balanced equation is \(\text{Na}_2\text{CO}_3 + 2\text{C}_{17}\text{H}_{35}\text{COOH} \rightarrow 2\text{C}_{17}\text{H}_{35}\text{COONa} + \text{CO}_2 + \text{H}_2\text{O}\).

Step-by-step solution

Write Down Reactants and Products

The reactants are sodium carbonate (\( ext{Na}_2 ext{CO}_3\)) and stearic acid (\( ext{C}_{17} ext{H}_{35} ext{COOH}\)). The product typically formed in this saponification reaction is soap (sodium stearate, \( ext{C}_{17} ext{H}_{35} ext{COONa}\)) and carbon dioxide (\( ext{CO}_2\)) and water (\( ext{H}_2 ext{O}\)).

Determine Reaction Components

For each molecule of sodium carbonate, two molecules of stearic acid are required to fully react, producing two molecules of sodium stearate, alongside a molecule each of water and carbon dioxide.

Write and Balance the Equation

The reaction equation starts with the reactants and ends with the products: \( ext{Na}_2 ext{CO}_3 + 2 ext{C}_{17} ext{H}_{35} ext{COOH} ightarrow 2 ext{C}_{17} ext{H}_{35} ext{COONa} + ext{CO}_2 + ext{H}_2 ext{O}\). Check to ensure that elements are balanced across the equation (same number of atoms on both sides).

Key concepts

Saponification

Saponification is a fascinating chemical reaction where fat or oil reacts with a strong base to produce soap and glycerol. In the context of the reaction between sodium carbonate and stearic acid, saponification plays a central role. Specifically, this process involves the hydrolysis of esters in the presence of a base to form alcohol and salt of the acid—in this case, the salt being soap. This reaction is what makes soaps soap-like and able to clean by emulsifying oils and dirt.
Stearic acid, a long-chain fatty acid, reacts with sodium carbonate, a common alkaline substance, to produce sodium stearate, which is a form of soap. This reaction not only forms soap but also releases carbon dioxide and water as by-products. A practical application of saponification is in making traditional soap at home, where oils like olive or coconut are reacted with a base such as sodium hydroxide.

Balancing Chemical Equations

Balancing chemical equations is crucial for accurately representing the conservation of mass in chemical reactions. When writing a chemical equation, it's vital to ensure that the number of each type of atom on the reactants side equals the number on the products side. This is known as balancing the equation.
In the exercise involving sodium carbonate and stearic acid, we begin by listing the reactants and products: sodium carbonate and stearic acid as reactants, and sodium stearate, carbon dioxide, and water as products. Initially, the reaction equation might look incomplete or inaccurate in terms of atom counts.

• The next step is adjusting coefficients to balance atoms on both sides.
• For this reaction, it takes two stearic acid molecules to react with one sodium carbonate molecule.
• This produces two molecules of sodium stearate, along with one molecule each of carbon dioxide and water.

The final balanced equation is: \[ \mathrm{Na}_2\mathrm{CO}_3 + 2 \mathrm{C}_{17}\mathrm{H}_{35}\mathrm{COOH} \rightarrow 2 \mathrm{C}_{17}\mathrm{H}_{35}\mathrm{COONa} + \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \] Ensuring each type of atom has equal numbers on both sides demonstrates understanding and precision in chemistry.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It enables chemists to predict the amounts of substances consumed and produced in a given reaction.
In the saponification reaction with sodium carbonate and stearic acid, stoichiometry helps calculate how much of each reactant is needed to produce a desired amount of product. By understanding the balanced chemical equation, we can determine the "molar ratio" of reactants to products.

• In this case, the balanced equation shows that one mole of sodium carbonate will react with two moles of stearic acid.
• This produces two moles of sodium stearate and one mole of carbon dioxide and water each.

Using stoichiometry, you can convert between moles of reactants and products, and with additional information, even calculate mass or volume.
This core concept helps not only in lab settings but also in industrial applications where chemical production needs to be scaled up efficiently.