Problem 135 - General Chemistry: Principles and Modern Applications

Question

When the equation below is balanced, the correct set of stoichiometric coefficients is (a) \(1,6 \longrightarrow 1,3,4;\) (b) \(1,4 \longrightarrow 1,2,2 ;\) (c) \(2,6 \longrightarrow 2,3,2;\) (d) \(3,8 \longrightarrow 3,4,2\) \(\begin{aligned} ? \mathrm{Cu}(\mathrm{s})+? \mathrm{HNO}_{3}(\mathrm{aq}) & \longrightarrow ? \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+? \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+? \mathrm{NO}(\mathrm{g}) \end{aligned}\)

Step-by-Step Solution

Answer

The correct set of stoichiometric coefficients for the balanced reaction is (d) 3,8 \longrightarrow 3,4,2

Step 1: Identify Reactants and Products

In this chemical reaction, the reactants are Cu(s) and HNO3(aq). The products are Cu(NO3)2(aq), H2O(l) and NO(g). First identify the number of atoms of each type on both sides of the reaction. For example, in the unbalanced equation, there is 1 copper (Cu) atom on the reactant side and 1 on the product side, 1 hydrogen (H) atom and 1 nitrogen (N) atom on the reactant side within the HNO3, and 3 oxygen (O) atoms on the reactant side while for the products, there are 2 hydrogen (H) atoms in H2O, 1 nitrogen (N) atom in NO and 5 oxygen (O) atoms.

Step 2: Find the Coefficients

Start balancing the atoms that appear in complex molecules or unknown coefficients. Begin with copper - it's already balanced with one atom on each side and doesn't show up anywhere else. Then look at hydrogen. There's one hydrogen in the reactants but two in the product (in H2O). Therefore, you need to update the coefficient for HNO3 to 2, which affects the nitrogen and oxygen counts as well and results in 2 hydrogen (H) atoms, 2 nitrogen (N) atoms, and 6 oxygen (O) atoms on the reactant side. Now look at nitrogen - there's 2 nitrogens in the reactants (in 2HNO3) and there are 2 nitrogens on the product side as well (1 in Cu(NO3)2 and 1 in NO), therefore it is already balanced. Lastly, look at oxygen - there are 6 on the reactant side, but only 5 on the product side. So you need to add a coefficient of 2 for NO to get an additional oxygen. But this affects nitrogen count as well, thus ending with three nitrogens in the reactants, so should have three nitrogens in the products. For that to happen, adjust the coefficient for Cu(NO3)2 to 3. Now the reaction is balanced.

Step 3: Write Down The Balanced Equation

The balanced equation should be \(3Cu(s) + 8HNO3(aq) \longrightarrow 3Cu(NO3)2(aq) + 4H2O(l) + 2NO(g)\). This guarantees that the atoms of each element are the same number on both the reactant and product sides.

Key Concepts

Stoichiometric Coefficients

Understanding stoichiometric coefficients is vital when dealing with chemical equations. These numerical values, placed in front of chemical compounds in a reaction, indicate the proportions in which reactants combine and products form. Consider them as the 'recipe' for a chemical reaction, telling you how many parts of each reactant you need and how many parts of each product you get.

For example, the equation \(2H_2 + O_2 \rightarrow 2H_2O\) uses stoichiometric coefficients to show that two molecules of hydrogen gas react with one molecule of oxygen gas to produce two molecules of water. In your exercise, finding the correct stoichiometric coefficients is like solving a puzzle where the goal is to preserve the mass and number of atoms across reactants and products.

Chemical Reaction

A chemical reaction is a process where substances, namely the reactants, undergo a reorganization of atoms to become different substances, known as the products. It's as if you're baking a cake—combining ingredients in specific proportions to create something new. In a chemical reaction, bonds are broken and new ones are formed, resulting in a change of the chemical substances.

There are many types of reactions, such as synthesis, decomposition, single replacement, and double replacement. The exercise you're working on involves a single replacement reaction, with copper displacing the hydrogen in nitric acid to form copper nitrate, water, and nitrogen monoxide.

Reactants and Products

Reactants are substances consumed to initiate a chemical reaction, like the flour, eggs, and sugar for your cake. On the opposite side, products are substances formed as a result of a chemical reaction—analogous to the cake itself. Balancing a chemical equation is analogous to ensuring you have the right amounts of ingredients to make the exact amount of cake you want, no more, no less.

In your exercise, the reactants are copper \( Cu(s) \) and nitric acid \( HNO_3(aq) \). The products are copper(II) nitrate \( Cu(NO_3)_2(aq) \), water \( H_2O(l) \), and nitrogen monoxide \( NO(g) \). It's a dance of swapping places and finding the right balance so that each atom that enters as a reactant makes its way into a product.

Chemical Equation Balancing

Balancing a chemical equation is like balancing a scale. The principle behind it is that the mass and the number of atoms of each element must remain constant throughout the reaction—this follows the Law of Conservation of Mass. You must ensure that whatever atoms go into the reaction come out of it, just rearranged into different compounds.

Use stoichiometric coefficients to achieve this balance. In the exercise, you start by identifying the types of atoms involved and then systematically adjust coefficients starting with the most complex species or those that appear in multiple reactants or products. By adding the coefficients step by step, you ensure that neither mass nor atoms are lost or gained, much like making sure every guest at a party has a dance partner.

Atomic Conservation

The concept of atomic conservation is the rulebook for balancing chemical equations. It dictates that atoms can neither be created nor destroyed in a chemical reaction. In other words, elements don't vanish or appear from thin air; they must be accounted for from the start of the reaction to the end.

In the process of balancing the equation in your exercise, atomic conservation serves as a checkpoint. After each adjustment of a stoichiometric coefficient, you'd reassess to ensure that each element's atom count remains consistent from reactants to products. It's a meticulous process, much like auditing where every penny must be accounted for. This principle reinforces the importance of balancing equations accurately to reflect what truly occurs in the chemical reaction.