Problem 79 - Chemistry and Chemical Reactivity

Question

Your body deals with excess nitrogen by excreting it in the form of urea, \(\mathrm{NH}_{2} \mathrm{CONH}_{2}\). The reaction producing it is the combination of arginine \(\left(\mathrm{C}_{6} \mathrm{H}_{14} \mathrm{N}_{4} \mathrm{O}_{2}\right)\) with water to give urea and ornithine \(\left(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{2}\right)\) $$ \mathrm{C}_{6} \mathrm{H}_{14} \mathrm{N}_{4} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}+\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{2} $$ arginine ornithine If you excrete 95 mg of urea, what mass of arginine must have been used? What mass of ornithine must have been produced?

Step-by-Step Solution

Answer

95 mg of urea corresponds to 0.275 g of arginine used and 0.209 g of ornithine produced.

Step 1: Calculate the Molar Mass of Urea

To find out the molar mass of urea \( \text{NH}_2\text{CONH}_2 \), add the atomic masses of all the atoms involved: - Nitrogen (N): 2 atoms \( \times 14\, \text{g/mol} = 28 \, \text{g/mol} \) - Hydrogen (H): 4 atoms \( \times 1\, \text{g/mol} = 4 \, \text{g/mol} \) - Carbon (C): 1 atom \( \times 12\, \text{g/mol} = 12 \, \text{g/mol} \) - Oxygen (O): 1 atom \( \times 16\, \text{g/mol} = 16 \, \text{g/mol} \)Calculating the total, the molar mass of urea is \( 28 + 4 + 12 + 16 = 60 \, \text{g/mol} \).

Step 2: Convert Mass of Urea to Moles

To find the moles of urea, use the mass given and the molar mass: \[ \text{moles of urea} = \frac{95\, \text{mg}}{60\, \text{g/mol}} \]Convert mg to g: \[ 95\, \text{mg} = 0.095\, \text{g} \]So, \[ \text{moles of urea} = \frac{0.095\, \text{g}}{60\, \text{g/mol}} = 0.00158\, \text{mol} \]

Step 3: Use Stoichiometry to Find Moles of Arginine

The chemical equation shows that 1 mole of arginine produces 1 mole of urea. Therefore, if you produce 0.00158 moles of urea, you must have used 0.00158 moles of arginine.

Step 4: Calculate the Molar Mass of Arginine

Calculate the molar mass of arginine (\( \text{C}_6\text{H}_{14}\text{N}_4\text{O}_2 \)) by adding:- Carbon (C): 6 atoms \( \times 12\, \text{g/mol} = 72 \, \text{g/mol} \)- Hydrogen (H): 14 atoms \( \times 1\, \text{g/mol} = 14 \, \text{g/mol} \)- Nitrogen (N): 4 atoms \( \times 14\, \text{g/mol} = 56 \, \text{g/mol} \)- Oxygen (O): 2 atoms \( \times 16\, \text{g/mol} = 32 \, \text{g/mol} \)Thus, the molar mass of arginine is \( 72 + 14 + 56 + 32 = 174 \, \text{g/mol} \).

Step 5: Calculate the Mass of Arginine Used

Use the moles of arginine and its molar mass to find the mass:\[ \text{mass of arginine} = 0.00158\, \text{mol} \times 174\, \text{g/mol} = 0.275\, \text{g} \].

Step 6: Use Stoichiometry to Find Moles and Mass of Ornithine

The reaction also produces 1 mole of ornithine for every mole of arginine used. So, 0.00158 moles of arginine will produce 0.00158 moles of ornithine.

Step 7: Calculate the Molar Mass of Ornithine

Add the atomic masses for ornithine \( \text{C}_5\text{H}_{12}\text{N}_2\text{O}_2 \):- Carbon (C): 5 atoms \( \times 12\, \text{g/mol} = 60 \, \text{g/mol} \)- Hydrogen (H): 12 atoms \( \times 1\, \text{g/mol} = 12 \, \text{g/mol} \)- Nitrogen (N): 2 atoms \( \times 14\, \text{g/mol} = 28 \, \text{g/mol} \)- Oxygen (O): 2 atoms \( \times 16\, \text{g/mol} = 32 \, \text{g/mol} \)Thus, the molar mass of ornithine is \( 60 + 12 + 28 + 32 = 132 \, \text{g/mol} \).

Step 8: Calculate the Mass of Ornithine Produced

Using the moles of ornithine and its molar mass:\[ \text{mass of ornithine} = 0.00158\, \text{mol} \times 132\, \text{g/mol} = 0.209\, \text{g} \].

Key Concepts

Molar Mass

To truly grasp the wonders of stoichiometry, understanding molar mass is crucial. Molar mass is the mass of one mole of a given substance. It's expressed in grams per mole (g/mol) and is calculated by adding up the atomic masses of all the atoms present in a molecular formula. For instance, let’s dissect the molar mass of urea, a compound vital in nitrogen metabolism.

Urea’s chemical formula is \( \mathrm{NH}_{2}\mathrm{CONH}_{2} \). To calculate its molar mass, we sum the atomic masses of its elements:

• Nitrogen (N): 2 atoms \( \times 14\, \text{g/mol} = 28 \text{ g/mol} \)
• Hydrogen (H): 4 atoms \( \times 1\, \text{g/mol} = 4 \text{ g/mol} \)
• Carbon (C): 1 atom \( \times 12\, \text{g/mol} = 12 \text{ g/mol} \)
• Oxygen (O): 1 atom \( \times 16\, \text{g/mol} = 16 \text{ g/mol} \)

This gives us a total molar mass of 60 g/mol for urea.

Understanding molar mass is essential for converting between the mass of a substance and the number of moles, a key aspect of stoichiometric calculations.

Chemical Equations

Chemical equations are the language of chemistry, depicting how substances react with each other to form new products. They do this by showing the reactants (starting materials) and products (ending materials) in a given reaction, using chemical symbols and formulas.

In this exercise, the chemical equation is:\[ \mathrm{C}_{6} \mathrm{H}_{14} \mathrm{N}_{4} \mathrm{O}_{2} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2} + \mathrm{C}_{5} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{2} \]This equation tells us that arginine and water react to produce urea and ornithine. Keeping the equation balanced is key, meaning the number and type of atoms must be the same on both sides. This reflects the conservation of mass—matter cannot be created or destroyed in a chemical reaction.

Chemical equations not only help visualize reactions but also guide stoichiometric calculations, allowing us to quantify amounts of reactants and products.

Nitrogen Metabolism

Nitrogen metabolism is a vital biological process, especially when considering compounds like urea produced as a result of breaking down amino acids in the liver. The excess nitrogen formed during protein breakdown needs to be excreted, and this is done effectively through the production of urea.

As seen in the exercise, arginine, an amino acid, is converted into urea and ornithine with the help of water. This process occurs in the urea cycle, a metabolic pathway that eliminates ammonia, a toxic byproduct of nitrogen metabolism. The chemical transformation of nitrogen into urea is crucial because urea is less toxic and can be safely excreted by the kidneys.

Understanding how nitrogen is processed and recycled in the body provides insight into how the body maintains balance and gets rid of potentially harmful substances.