Question

Aspirin $\left({\mathrm{C}}_9{\mathrm{H}}_8{\mathrm{O}}_4\right)$ is synthesized by reacting salicylic acid $\left({\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3\right)$ with acetic anhydride $\left({\mathrm{C}}_4{\mathrm{H}}_6{\mathrm{O}}_3\right).$ The balanced equation is $${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3+{\mathrm{C}}_4{\mathrm{H}}_6{\mathrm{O}}_3⟶{\mathrm{C}}_9{\mathrm{H}}_8{\mathrm{O}}_4+{\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$$ a. What mass of acetic anhydride is needed to completely consume $1.00\times {10}^2$ g salicylic acid? b. What is the maximum mass of aspirin (the theoretical yield) that could be produced in this reaction?

Short answer

a. To completely consume $1.00\times {10}^2$ g salicylic acid, the mass of acetic anhydride needed is: $$\text{mass}=n\times M=\frac{1.00\times {10}^2\text{g}}{138.12\text{g/mol}}\times 102.09\text{g/mol}$$ b. The maximum mass of aspirin (theoretical yield) that can be produced is: $$\text{mass}=n\times M=\frac{1.00\times {10}^2\text{g}}{138.12\text{g/mol}}\times 180.16\text{g/mol}$$

Step-by-step solution

Calculate moles of given salicylic acid

We are given the mass of salicylic acid to be $1.00\times {10}^2$ grams. To determine the moles of the salicylic acid, we will use its molar mass: $${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3\to 7(12.01)+6(1.01)+3(16.00)=138.12\mathrm{g}/\mathrm{mol}$$ Now, calculate the moles of salicylic acid: $$n=\frac{m}{M}=\frac{1.00\times {10}^2\text{g}}{138.12\text{g/mol}}$$

Calculate moles of acetic anhydride required to react completely with salicylic acid

According to the stoichiometry of the balanced equation, 1 mole of salicylic acid reacts completely with 1 mole of acetic anhydride. Therefore, the moles of acetic anhydride needed are equal to the moles of salicylic acid calculated in step 1.

Calculate the mass of acetic anhydride needed

Now, we need to convert the moles of acetic anhydride to its mass. First, we find the molar mass of acetic anhydride: $${\mathrm{C}}_4{\mathrm{H}}_6{\mathrm{O}}_3\to 4(12.01)+6(1.01)+3(16.00)=102.09\mathrm{g}/\mathrm{mol}$$ Now, we will multiply the moles of acetic anhydride calculated in step 2 by its molar mass to get the mass of acetic anhydride: $$\text{mass}=n\times M$$

Determine the maximum mass of aspirin that can be produced

According to stoichiometry, 1 mole of salicylic acid will produce 1 mole of aspirin. Therefore, the moles of aspirin produced will be equal to moles of salicylic acid. Next, we will find the molar mass of aspirin: $${\mathrm{C}}_9{\mathrm{H}}_8{\mathrm{O}}_4\to 9(12.01)+8(1.01)+4(16.00)=180.16\mathrm{g}/\mathrm{mol}$$ Now, we will multiply the moles of aspirin by its molar mass to get the maximum mass of aspirin (theoretical yield) that can be produced. $$\text{mass}=n\times M$$

Key concepts

Theoretical Yield

Theoretical yield is a key concept in stoichiometry, which is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It refers to the maximum amount of product that can be obtained from a given amount of reactants, assuming the reaction goes to completion without any loss or side reactions. When calculating theoretical yield, you start by determining the number of moles of each reactant involved in the reaction based on their molar masses. Then, using the balanced chemical equation, you figure out how the reactants convert into products. In this particular exercise on aspirin synthesis, the balanced chemical equation shows that one mole of salicylic acid reacts with one mole of acetic anhydride to produce one mole of aspirin. Understanding the concept of theoretical yield helps you set realistic expectations of how much product you'll obtain in an ideal scenario. It's a crucial step in planning chemical syntheses and calculating efficiencies later on, as the actual yield obtained from a reaction is often less due to various practical limitations.

Molar Mass

Molar mass is a vital concept in understanding chemical reactions and stoichiometry. It is the mass of a given substance (chemical element or chemical compound) divided by the amount of substance, measured in g/mol. Molar mass allows chemists to convert between the mass of a substance and the amount in moles, which is essential for stoichiometric calculations. In our aspirin synthesis example, the molar mass of each component plays a significant role. To find the molar mass of a compound, you sum up the atomic masses of all the atoms in its molecular formula. For instance, the molar mass of salicylic acid (${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3$) is calculated by adding together the atomic masses of carbon, hydrogen, and oxygen multiplied by their respective numbers in the formula: $$7(12.01)+6(1.01)+3(16.00)=138.12\mathrm{g}/\mathrm{mol}$$ Having accurate molar masses allows you to determine the moles of reactants and products in a reaction, necessary for calculating theoretical yields. Moreover, being proficient with molar mass calculations enhances your understanding of chemical quantities and relationships within reactions.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, are transformed into different substances, called products. This transformation involves breaking chemical bonds in the reactants and forming new bonds in the products. It is generally represented by a chemical equation that clearly depicts the reactants and products with their respective coefficients, which indicate the ratio of moles involved in the reaction.In the provided aspirin synthesis reaction: $${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3+{\mathrm{C}}_4{\mathrm{H}}_6{\mathrm{O}}_3⟶{\mathrm{C}}_9{\mathrm{H}}_8{\mathrm{O}}_4+{\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$$ Each reactant and product is shown with its molecular formula, and they are balanced to respect the conservation of mass and atoms. This means the number of each type of atom on the reactant side is equal to the number on the product side, maintaining the integrity of matter. Balanced chemical equations are crucial for stoichiometry, as they provide the necessary proportions essential for calculating the theoretical yield and understanding the reaction's mechanics. In stoichiometric calculations, these equations guide how much of each reactant is needed and how much of each product can be expected, presenting a clear chemical storyline from start to finish.