Problem 1 - General Chemistry: Principles and Modern Applications

Question

Balance the following equations by inspection. (a) \(\mathrm{SO}_{3} \longrightarrow \mathrm{SO}_{2}+\mathrm{O}_{2}\) (b) \(\mathrm{Cl}_{2} \mathrm{O}_{7}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HClO}_{4}\) (c) \(\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HNO}_{3}+\mathrm{NO}\) (d) \(\mathrm{PCl}_{3}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{3}+\mathrm{HCl}\)

Step-by-Step Solution

Answer

The balanced equations are: (a) \(2\mathrm{SO}_{3} \longrightarrow 2\mathrm{SO}_{2}+\mathrm{O}_{2}\) (b) \(2\mathrm{Cl}_{2} \mathrm{O}_{7} + 8\mathrm{H}_{2} \mathrm{O} \longrightarrow 8\mathrm{HClO}_{4}\) (c) \(3\mathrm{NO}_{2}+ \mathrm{H}_{2} \mathrm{O} \longrightarrow 2\mathrm{HNO}_{3}+ \mathrm{NO}\) (d) \( \mathrm{PCl}_{3} + 3 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{3}+ 3\mathrm{HCl}\)

Step 1 - Examining and Balancing equation (a)

In the given equation \(\mathrm{SO}_{3} \longrightarrow \mathrm{SO}_{2}+\mathrm{O}_{2}\), count the number of each element on both sides. On the left, there are 1 sulfur and 3 oxygen atoms. On the right side, there are 1 sulfur, 2 oxygen from \(\mathrm{SO}_{2}\) and 2 from \(\mathrm{O}_{2}\) totaling to 4 oxygen atoms. Place the coefficient 2 in front of \(\mathrm{SO}_{3}\) and \(\mathrm{SO}_{2}\) to balance the number of Sulfur and Oxygen atoms. The balanced chemical equation is \(2\mathrm{SO}_{3} \longrightarrow 2\mathrm{SO}_{2}+\mathrm{O}_{2}\).

Step 2 - Examining and Balancing equation (b)

In the equation \(\mathrm{Cl}_{2} \mathrm{O}_{7}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HClO}_{4}\), there are 2 Chlorine, 7 Oxygen and 2 Hydrogen atoms on the left side and on the right side, there is 1 Chlorine, 4 Oxygen and 1 Hydrogen atom. Adjust the coefficients to make the numbers of atoms the same on both sides of the equation. The balanced equation is \(2\mathrm{Cl}_{2} \mathrm{O}_{7} + 8\mathrm{H}_{2} \mathrm{O} \longrightarrow 8\mathrm{HClO}_{4}\).

Step 3 - Examining and Balancing equation (c)

In the equation \(\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HNO}_{3}+\mathrm{NO}\), there are 1 Nitrogen, 2 Oxygen and 2 Hydrogen atoms on the left side and on the right side, there are 2 Nitrogen, 4 Oxygen and 1 Hydrogen atoms. Again, adjust coefficients so that the numbers of each type of atom match on both sides. The balanced equation is \(3\mathrm{NO}_{2}+ \mathrm{H}_{2} \mathrm{O} \longrightarrow 2\mathrm{HNO}_{3}+ \mathrm{NO}\).

Step 4 - Examining and Balancing equation (d)

In the equation \(\mathrm{PCl}_{3}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{3}+\mathrm{HCl}\), there is 1 Phosphorus, 3 Chlorine and 2 Hydrogen atoms on the left side and on the right side, there is 1 Phosphorus, 1 Chlorine, 3 Hydrogen atoms from \(\mathrm{H}_{3} \mathrm{PO}_{3}\) and 1 from \(\mathrm{HCl}\) totaling to 4 Hydrogen and 3 Oxygen atoms. Adjust the coefficients to balance the equation, which is \( \mathrm{PCl}_{3} + 3 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{3}+ 3\mathrm{HCl}\).

Key Concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is an essential concept because it allows chemists to predict the amounts of substances consumed and produced in given reactions. Understanding stoichiometry helps to determine the proportions in which chemicals will combine and react.

Key aspects of stoichiometry include:

• **Mole Ratios:** These are derived from the coefficients of the balanced equation and indicate the ratio of moles of each substance involved in the reaction.
• **Mass Conservation:** Stoichiometry ensures that the mass, as well as the number of atoms, remains constant throughout the reaction as per the Law of Conservation of Mass.
• **Practical Applications:** It is crucial in calculating reactant quantities for reactions in industry and laboratory settings.

Remember, stoichiometry is the tool used to balance chemical equations, illustrating how various substances relate to each other quantitatively in reactions.

Chemical Reactions

Chemical reactions involve the transformation of substances through breaking and forming chemical bonds. A reactant is a substance that starts a chemical reaction, and a product is what you end up with after the reaction.

Some important features of chemical reactions include:

• **Reactants and Products:** Chemical reactions begin with reactants that undergo change to form products.
• **Conservation:** During the reaction, there is a conservation of atoms; they are rearranged but neither created nor destroyed.
• **Energy Changes:** Reactions often involve energy changes in the form of heat, light, or electricity.

For example, in the reaction of sulfur trioxide (\(\mathrm{SO}_3\)) being transformed into sulfur dioxide (\(\mathrm{SO}_2\)) and oxygen (\(\mathrm{O}_2\)), we see clear examples of how molecules can break apart and recombine to result in new chemical configurations.

Chemical Equation Balancing Steps

Balancing chemical equations is a practice important for upholding the Law of Conservation of Mass. It involves making sure each element has the same number of atoms on both sides of the equation. Here’s a simplified sequence to follow:

• **Count Atoms:** First, list all the elements and count the number of atoms for each element in both the reactants and the products.
• **Adjust Coefficients:** Use coefficients to adjust the number of molecules (atoms) to ensure the same number of each type of element on both sides of the equation.
• **Check Your Work:** After balancing, recalculate the number of atoms for each element to verify both sides are equal.

For example, in equation (a):\(\mathrm{SO}_3 \longrightarrow \mathrm{SO}_2 + \mathrm{O}_2\)adjusting coefficients to\(2\mathrm{SO}_3 \longrightarrow 2\mathrm{SO}_2 + \mathrm{O}_2\)ensures that the number of sulfur and oxygen atoms are balanced on both sides. Following these steps helps in accurately representing chemical reactions.