One of the most bizarre reactions in chemistry is called the Ugi reaction: $$ \begin{array}{l}{\mathrm{R}_{1} \mathrm{C}(=\mathrm{O}) \mathrm{R}_{2}+\mathrm{R}_{3}-\mathrm{NH}_{2}+\mathrm{R}_{4} \mathrm{COOH}+\mathrm{R}_{5} \mathrm{NC} \rightarrow} \\ {\mathrm{R}_{4} \mathrm{C}(=\mathrm{O}) \mathrm{N}\left(\mathrm{R}_{3}\right) \mathrm{C}\left(\mathrm{R}_{1} \mathrm{R}_{2}\right) \mathrm{C}=\mathrm{ONHR}_{5}+\mathrm{H}_{2} \mathrm{O}}\end{array} $$ (a) Write out the balanced chemical equation for the Ugi reaction, for the case where \(R=C H_{3} C H_{2} C H_{2} C H_{2} C H_{2} C H_{2}-\) (this is called the hexyl group) for all compounds. (b) What mass of the "hexyl Ugi product" would you form if 435.0 \(\mathrm{mg}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) was the limiting reactant?

We replace all the R groups in the chemical equation with the hexyl group CH3CH2CH2CH2CH2CH2-. The reaction will be: $$ \begin{array}{l}{\mathrm{HexCO}+\mathrm{HexNH}_{2}+\mathrm{HexCOOH}+\mathrm{HexNC} \rightarrow} \\\ {\mathrm{Hex}\mathrm{C}(=\mathrm{O}) \mathrm{N}\left(\mathrm{Hex}\right) \mathrm{C}\left(\mathrm{Hex}\mathrm{Hex}\right) \mathrm{C}=\mathrm{ONHex}+\mathrm{H}_{2} \mathrm{O}}\end{array} $$

First, we need to find the molecular weight of the limiting reactant (HexNH2) and the hexyl Ugi product: Molar mass of HexNH2 = \( 6 \times 12.01 + 13 \times 1.008 + 1 \times 14.01 = 101.198 \) g/mol Molar mass of hexyl Ugi product = \( (Tree\:of\:hexyl\:groups\:24 \times 12.01 + 50 \times 1.008) + (4 \times 14.01) = 397.454 \) g/mol Next, we will calculate the number of moles of HexNH2 (limiting reactant) and then determine the number of moles of the hexyl Ugi product formed using stoichiometry. Lastly, we will convert the number of moles of the hexyl Ugi product to mass using its molar mass. Moles of HexNH2 = \( \frac{435.0 \;mg}{101.198\ g/mol \times 1000\ \frac{mg}{g}} = 0.00430 \) mol According to the balanced chemical equation, moles of hexyl Ugi product = moles of HexNH2 Moles of hexyl Ugi product = 0.00430 mol Finally, we can find out the mass of the hexyl Ugi product formed: Mass of hexyl Ugi product = moles of hexyl Ugi product × molar mass of hexyl Ugi product = 0.00430 mol * 397.454 g/mol ≈ 1.71 g