A sink drain can become clogged with solid fat such as glyceryl tristearate (tristearin).
c. How many milliliters of a 0.500 M NaOH solution are needed to completely react with 10.0 g of glyceryl tristearate (tristearin)?

Verified step by step guidance

1. Step 1: Write the balanced chemical equation for the reaction. Glyceryl tristearate (C57H110O6) reacts with sodium hydroxide (NaOH) in a saponification reaction to produce glycerol (C3H8O3) and sodium stearate (C18H35O2Na). The balanced equation is: $C{57}_{110}{O}_6+3\mathrm{NaOH}\to C{3}_8{O}_3+3C{18}_{35}{O}_2\mathrm{Na}$.
2. Step 2: Calculate the molar mass of glyceryl tristearate (C57H110O6). Add the atomic masses of all the atoms in the molecule: $57\times 12.01+110\times 1.008+6\times 16.00$. This gives the molar mass in grams per mole.
3. Step 3: Convert the given mass of glyceryl tristearate (10.0 g) to moles using its molar mass. Use the formula: $\frac{\mathrm{mass}}{\mathrm{molar} \mathrm{mass}}$. Substitute the values to find the number of moles of glyceryl tristearate.
4. Step 4: Use the stoichiometry of the reaction to determine the moles of NaOH required. From the balanced equation, 1 mole of glyceryl tristearate reacts with 3 moles of NaOH. Multiply the moles of glyceryl tristearate by 3 to find the moles of NaOH needed.
5. Step 5: Calculate the volume of 0.500 M NaOH solution required to provide the necessary moles of NaOH. Use the formula: $\frac{\mathrm{moles}}{\mathrm{molarity}}$. Substitute the moles of NaOH and the molarity (0.500 M) to find the volume in liters, then convert to milliliters by multiplying by 1000.

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate how much of a substance is needed or produced in a reaction based on balanced chemical equations. Understanding stoichiometry is essential for determining the amount of NaOH required to react with glyceryl tristearate.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (M). In this question, the 0.500 M NaOH solution indicates that there are 0.500 moles of NaOH in every liter of solution, which is crucial for calculating the volume needed to react with a specific mass of glyceryl tristearate.

Chemical Reaction of Saponification

The saponification reaction involves the hydrolysis of fats or oils in the presence of a strong base, such as NaOH, resulting in the formation of glycerol and soap. Glyceryl tristearate, a triglyceride, undergoes saponification when reacted with NaOH. Understanding this reaction is key to determining how much NaOH is required to completely react with the given mass of glyceryl tristearate.