Question

Balance the reaction for the synthesis of urea, commonly used as a fertilizer: $$ \mathrm{CO}_{2}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

Balanced equation: \( \mathrm{CO}_{2} + 2\mathrm{NH}_{3} \rightarrow \mathrm{NH}_{2}\mathrm{CONH}_{2} + \mathrm{H}_{2}\mathrm{O} \).

Step-by-step solution

Write Down Unbalanced Equation

First, write down the unbalanced chemical equation for the synthesis of urea for easy reference: \( \mathrm{CO}_{2}(g) + \mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(s) + \mathrm{H}_{2} \mathrm{O}(l) \).

Count Atoms for Each Element

Count the number of atoms of each element on both the reactant and product sides. Reactants have 1 C, 2 O, 1 N, and 3 H (from ammonia), while the products have 1 C, 1 N (urea), 1 N (free nitrogen), 1 O, and 2 H (urea and additional water).

Balance Nitrogen Atoms

There are more nitrogen atoms on the product side due to the separate NH groups in the urea and ammonia. Use 2 \( \mathrm{NH}_{3} \) to match this: \( \mathrm{CO}_{2}(g) + 2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{2}\mathrm{CONH}_{2}(s) + \mathrm{H}_{2}\mathrm{O}(l) \).

Adjust Water Molecule

After balancing nitrogen, count hydrogen to see if there is a need for additional molecules. Hydrogens are already balanced using 2 \( \mathrm{NH}_{3} \).

Verify Oxygen and Final Check

Currently, there are 2 oxygen atoms in CO2 and 1 oxygen in both urea and water. Ensure each side has equivalent counts: product side addresses both carbons and oxygen appropriately, confirming the equation is balance.

Key concepts

Chemical Equations

In chemistry, a chemical equation is a symbolic representation of a chemical reaction. It displays the starting materials or reactants on the left and the resulting substances or products on the right. An arrow typically separates these two parts, indicating the direction of the reaction. For example, in the synthesis of urea, the unbalanced equation is:
\[ \mathrm{CO}_{2}(g) + \mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(s) + \mathrm{H}_{2} \mathrm{O}(l) \]
Balancing chemical equations is essential because it follows the Law of Conservation of Mass. This law dictates that matter cannot be created or destroyed in a chemical reaction. Thus, the same number of each type of atom must appear on both sides of the equation. When balancing equations, you'll typically start by listing out the number of each type of atom on both sides of the equation and iteratively adjust the coefficients in front of compounds to ensure balance.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the reactants and products in a chemical reaction. It's essentially about counting atoms and ensuring that the reaction complies with the Law of Conservation of Mass.
One key concept in stoichiometry is the use of coefficients to balance a chemical equation. Coefficients are numbers placed in front of the chemical formulas in an equation to indicate the number of molecules or moles of each compound. In the balanced equation for urea synthesis, the coefficients indicate how many units of each substance are involved in the reaction.

• Chemists use stoichiometric coefficients to predict the amounts of products generated from a given amount of reactants.
• These coefficients also help determine limiting reactants and calculate the theoretical yields and percent yields of reactions.

With practice, stoichiometry becomes an invaluable tool for understanding and predicting chemical reactions.

Urea Synthesis

Urea synthesis is an important industrial chemical process. It was first artificially synthesized by Friedrich Wöhler in 1828. This process is integral to producing fertilizers widely used in agriculture.
The reaction involves the synthesis of urea \( \mathrm{NH}_{2} \mathrm{CONH}_{2} \) from carbon dioxide \( \mathrm{CO}_{2} \) and ammonia \( \mathrm{NH}_{3} \). The broader reaction can be simplified to:

• Carbon dioxide is a colorless gas and a byproduct of respiration and fossil fuel combustion.
• Ammonia is a pungent, colorless gas that serves as a critical nitrogen source in the reaction.

In the balanced chemical equation:
\[ \mathrm{CO}_{2}(g) + 2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{2} \mathrm{CONH}_{2}(s) + \mathrm{H}_{2} \mathrm{O}(l) \]
The equation implies that one molecule of carbon dioxide reacts with two molecules of ammonia to produce one molecule of urea and one molecule of water. This synthesis highlights how human ingenuity can transform raw materials into useful products.