Question

Billions of pounds of urea are produced annually for use as fertilizer. Balance the skeletal equation for the synthesis of urea. $$ \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

The balanced equation is \[ 2\mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{CO}(\mathrm{NH}_{2})_{2}(s)+2\mathrm{H}_{2} \mathrm{O}(l) \

Step-by-step solution

Verify the number of atoms on both sides

Count and list the number of each atom on both sides of the equation to see which are not balanced.

Balance carbon atoms

Start with carbon atoms since they appear only once on both sides of the equation. They are already balanced, with one carbon atom on each side.

Balance hydrogen atoms

Next, balance the hydrogens. On the left, there are 3 hydrogens from NH3 and two on the right side from NH2 and one from H2O. We need to double the NH3 and H2O to balance hydrogen atoms.

Balance nitrogen atoms

Now, balance nitrogen atoms. There are two nitrogen atoms in the urea molecule on the right, so we need to have two NH3 molecules on the left.

Balance oxygen atoms

Lastly, balance oxygen atoms. We have two on both sides, so they are already balanced.

Write the balanced equation

Now that all atoms are balanced, write the balanced chemical equation.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. The fundamental principle of stoichiometry is based on the law of conservation of mass that states that matter cannot be created nor destroyed in a chemical reaction. Therefore, the mass of the reactants must equal the mass of the products.

In balancing chemical equations, stoichiometry allows us to quantify the proportions of elements and compounds involved. It operates through coefficients—simple whole numbers placed in front of chemical formulas in an equation to indicate the relative number of moles of each reactant and product. For example, in the urea synthesis exercise, the coefficient '2' in front of NH3 and H2O ensures that there are enough hydrogen atoms to balance the equation.

Understanding stoichiometry is crucial, not just for completing a balanced equation but also for real-world applications like determining the amount of each substance needed for a chemical reaction or analyzing the yield of a product from a given amount of reactants.

Chemical Reaction

A chemical reaction is a process that transforms one set of chemical substances, the reactants, into another set, the products. Reactions involve the breaking and forming of chemical bonds, leading to changes in the composition of matter. Reactions are depicted by chemical equations that have reactants on the left, products on the right, and an arrow that points from reactants to products to indicate the direction of the transformation.

In the exercise involving urea synthesis, ammonia (NH3) and carbon dioxide (CO2) react to form urea (CO(NH2)2) and water (H2O). This type of reaction is a synthesis reaction, where simpler substances combine to form a more complex compound. By balancing the equation, we ensure that the equation accurately represents the conservation of atoms during the reaction. Recognizing different types of reactions and their distinctive patterns can significantly enhance a student's ability to balance chemical equations and understand the processes occurring at a molecular level.

Chemical Formula

A chemical formula represents the composition of a substance using symbols for its constituent elements and numerical subscripts to indicate the number of atoms of each element in one molecule of the substance. It is a shorthand way to convey detailed information about a compound's structure. For instance, the formula for water, H2O, tells us that each molecule consists of two hydrogen atoms bonded to one oxygen atom.

In chemical reactions, the reactants and products are written using their chemical formulas, as seen in the urea production exercise. The correct interpretation of these formulas is pivotal when identifying what and how many atoms need to be balanced. Misunderstanding a formula could lead to incorrect balancing of the equation, hence a solid grasp of chemical formulas is integral to the study of chemistry. Learning to recognize and write correct chemical formulas is a foundational skill in chemistry that enables students to communicate complex information succinctly and accurately.