Question

One of the most bizarre reactions in chemistry is called the Ugi reaction: \(\mathrm{R}_{1} \mathrm{C}(=\mathrm{O}) \mathrm{R}_{2}+\mathrm{R}_{3}-\mathrm{NH}_{2}+\mathrm{R}_{4} \mathrm{COOH}+\mathrm{R}_{5} \mathrm{NC} \rightarrow\) \(\mathrm{R}_{4} \mathrm{C}(=\mathrm{O}) \mathrm{N}\left(\mathrm{R}_{3}\right) \mathrm{C}\left(\mathrm{R}_{1} \mathrm{R}_{2}\right) \mathrm{C}=\mathrm{ONHR}_{5}+\mathrm{H}_{2} \mathrm{O}\) (a) Write out the balanced chemical equation for the Ugi reaction, for the case where \(\mathrm{R}=\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2}-\) (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?

Short answer

(a) The balanced chemical equation for the hexyl Ugi reaction is: \[1~Hexyl ~ketone + 1 ~Hexyl ~amine + 1 ~Hexyl ~acid + 1 ~Hexyl ~isocyanide \rightarrow 1 ~Hexyl ~Ugi ~Product + 1 ~H_2O\] (b) The mass of the hexyl Ugi product formed when 435.0 mg of hexyl amine is the limiting reactant is 800 mg.

Step-by-step solution

Write the balanced chemical equation

The given Ugi reaction can be modified by attaching the hexyl group (CH3CH2CH2CH2CH2CH2-) to all compounds: \[R_1 CO R_2 + R_3 NH_2 + R_4 COOH + R_5 NC \rightarrow R_4 C(=O) N(R_3) C(R_1 R_2) C=ONHR_5 + H_2O\] Replace R with the hexyl group CH3CH2CH2CH2CH2CH2- \[CH_3CH_2CH_2CH_2CH_2CH_2 CO CH_3CH_2CH_2CH_2CH_2CH_2 + CH_3CH_2CH_2CH_2CH_2CH_2 NH_2 + CH_3CH_2CH_2CH_2CH_2CH_2 COOH + CH_3CH_2CH_2CH_2CH_2CH_2 NC \rightarrow\] \[CH_3CH_2CH_2CH_2CH_2CH_2 C(=O) N(CH_3CH_2CH_2CH_2CH_2CH_2) C(CH_3CH_2CH_2CH_2CH_2CH_2 CO CH_3CH_2CH_2CH_2CH_2CH_2) C=ONHCH_3CH_2CH_2CH_2CH_2CH_2 + H_2O\] Now, the balanced chemical equation for the hexyl Ugi reaction is: \[1~Hexyl ~ketone + 1 ~Hexyl ~amine + 1 ~Hexyl ~acid + 1 ~Hexyl ~isocyanide \rightarrow 1 ~Hexyl ~Ugi ~Product + 1 ~H_2O\]

Calculate molecular weights

Calculate the molecular weights of hexyl amine and hexyl Ugi product for further calculations. For hexyl amine (CH3CH2CH2CH2CH2CH2NH2): 1 nitrogen atom: 1 * 14.01 = 14.01 g/mol 7 carbon atoms: 7 * 12.01 = 84.07 g/mol 17 hydrogen atoms: 17 * 1.01 = 17.17 g/mol Molecular weight of hexyl amine = 14.01 + 84.07 + 17.17 = 115.25 g/mol For hexyl Ugi product (Hexyl imidazolidinone derivative): 1 nitrogen atom: 1 * 14.01 = 14.01 g/mol 13 carbon atoms: 13 * 12.01 = 156.13 g/mol 26 hydrogen atoms: 26 * 1.01 = 26.26 g/mol 1 oxygen atom: 1 * 16.00 = 16.00 g/mol Molecular weight of hexyl Ugi product = 14.01 + 156.13 + 26.26 + 16.00 = 212.40 g/mol

Calculate the mass of hexyl Ugi product

Now, use stoichiometry of the balanced chemical equation to calculate the mass of hexyl Ugi product formed. Given mass of hexyl amine = 435.0 mg From the balanced equation, 1 mol of hexyl amine reacts to form 1 mol of hexyl Ugi product. Moles of hexyl amine = mass / molecular weight = (435.0 mg) / (115.25 g/mol) = 0.00377 mol (divide by 1000 to convert mg to g) Moles of hexyl Ugi product formed = moles of hexyl amine = 0.00377 mol Mass of hexyl Ugi product formed = moles * molecular weight = (0.00377 mol) * (212.40 g/mol) = 0.800 g (multiply by 1000 to convert g to mg) So, the mass of the hexyl Ugi product formed is 800 mg.

Key concepts

Balanced Chemical Equation

In chemical reactions, it's crucial to ensure that the number of atoms of each element is the same on both sides of the equation. This is called balancing a chemical equation. During the Ugi reaction, we start with specific reactants and end up forming a product. Let’s look at the original reaction without substituents:

• Keto function \(\mathrm{R}_{1} \mathrm{C}(=\mathrm{O}) \mathrm{R}_{2}\) attaches to an amine \(\mathrm{R}_{3}-\mathrm{NH}_{2}\).
• The carboxylic acid \(\mathrm{R}_{4} \mathrm{COOH}\) combines with an isocyanide \(\mathrm{R}_{5} \mathrm{NC}\).

To balance the chemical equation, ensure each type of atom appears equally on both sides. When we replace all \(\mathrm{R}\) groups with hexyl groups, this becomes simpler. One molecule of each reactant: hexyl ketone, hexyl amine, hexyl acid, and hexyl isocyanide will react to form a single molecule of the hexyl Ugi product, along with one water molecule. Remember, balancing is not just about equal numbers of atoms, but also about consistent chemical formulas, helping predict how much product can be formed.

Molecular Weight Calculation

Calculating the molecular weight (or molecular mass) of a compound is a fundamental aspect of chemistry. It involves summing the atomic weights of all atoms in a molecule. Let’s take hexyl amine (\(\mathrm{CH}_{3}\mathrm{CH}_{2}\mathrm{CH}_{2}\mathrm{CH}_{2}\mathrm{CH}_{2}\mathrm{CH}_{2}\mathrm{NH}_{2}\)) as an example:

• It contains 1 nitrogen atom (14.01 g/mol),
• 7 carbon atoms (84.07 g/mol), and
• 17 hydrogen atoms (17.17 g/mol).

Adding these gives us the molecular weight of hexyl amine: 115.25 g/mol. To handle more complex compounds like the hexyl Ugi product, tally the weight of nitrogen, carbon, hydrogen, and oxygen atoms. Always ensure that every atom's weight from the periodic table is included. Precise molecular weights are essential for determining how much of each reactant is needed and can also help predict amounts of products, like in stoichiometry.

Stoichiometry

In stoichiometry, the balanced chemical equation is used to calculate reactants and products in a chemical reaction. It is all about the proportional relationships between substances. According to our balanced Ugi reaction, every mole of reactants produces equal moles of product. This one-to-one mole ratio simplifies calculations.
Consider hexyl amine as the limiting reactant in the Ugi reaction. If 435 mg of hexyl amine is used, convert this mass to moles by dividing by its molecular weight (115.25 g/mol). Converting 435 mg to grams gives us 0.435 g, and calculating the moles gives:\[ \text{Moles} = \frac{0.435}{115.25} = 0.00377 \text{ mol} \] Using the one-to-one stoichiometric ratio from the balanced equation, these moles of hexyl amine form the same moles of hexyl Ugi product. Multiply this by the product’s molecular weight (212.40 g/mol) to find the mass of the product formed:
\[ \text{Mass} = 0.00377 \times 212.40 = 0.800 \text{ g or 800 mg} \] This understanding allows chemists to predict yields and amounts in reactions accurately using stoichiometry.