High-temperature superconducting oxides hold great promise in the utility, transportation, and computer industries

(a) One superconductor is $\mathrm{La}_{2-x} \mathrm{Sr}_{x} \mathrm{CuO}_{4}$ . Calculate the molar

masses of this oxide when $x=0, x=1,$ and $x=0.163$

(b) Another common superconducting oxide is made by heating a mixture of barium carbonate, copper(II) oxide, and ytrium(III) oxide, followed by further heating in $\mathrm{O}_{2}$ :

$$

4 \mathrm{BaCO}_{3}(s)+6 \mathrm{CuO}(s)+\mathrm{Y}_{2} \mathrm{O}_{3}(s) \longrightarrow

$$

$$

2 \mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{65}(s)+4 \mathrm{CO}_{2}(g)

$$

$$

2 \mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{6.5}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}(s)

$$

When equal masses of the three reactants are heated, which reactant is limiting?

(c) After the product in part (b) is removed, what is the mass $\%$ of each reactant in the remaining solid mixture?

## Discussion

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Aspirin can be made in the laboratory by reacting acetic anhydride $\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)$ with salicylic acid $\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)$ to form aspirin $\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)$ and acetic acid $\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\right) .$ The balanced equation is:

$$\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$

In a laboratory synthesis, a student begins with 3.00 $\mathrm{mL}$ of acetic anhydride (density $=1.08 \mathrm{g} / \mathrm{mL} )$ and 1.25 $\mathrm{g}$ of salicylic acid.Once the reaction is complete, the student collects 1.22 $\mathrm{g}$ of aspirin. Determine the limiting reactant, theoretical yield of aspirin, and percent yield for the reaction.

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} \longrightarrow \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?

You take 1.00 g of an aspirin tablet (a compound consisting solely of carbon, hydrogen, and oxygen), burn it in air, and collect 2.20 $\mathrm{g} \mathrm{CO}_{2}$ and 0.400 $\mathrm{g} \mathrm{H}_{2} \mathrm{O} .$ You know that the molar mass of aspirin is between 170 and 190 $\mathrm{g} / \mathrm{mol}$ . Reacting 1 $\mathrm{mole}$ of salicylic acid with 1 mole of acetic anhydride $\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)$ gives you 1 mole of aspirin and 1 mole of acetic acid $\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\right)$ Use this information to determine the molecular formula of salicylic acid.

The aspirin substitute, acetaminophen $\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}\right),$ is produced by the following three-step synthesis:

$$

\mathrm{I} . \quad \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}(s)+3 \mathrm{H}_{2}(g)+\mathrm{HCl}(a q) \longrightarrow

$$

$$

\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)

$$

$$

\mathrm{II}\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+\mathrm{NaOH}(a q) \longrightarrow

$$

$$

\mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q)

$$

$$

\mathrm{III.} \quad \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow

$$

$$

\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}(s)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l)

$$

The first two reactions have percent yields of 87$\%$ and 98$\%$ by mass, respectively. The overall reaction yields 3 moles of acetaminophen product for every 4 moles of $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}$ reacted.

a. What is the percent yield by mass for the overall process?

b. What is the percent yield by mass of Step III?