Problem 46 - Chemistry Matter and Change

Question

When solid copper is added to nitric acid, copper(II) nitrate, nitrogen dioxide, and water are produced. Write the balanced chemical equation for the reaction. List six mole ratios for the reaction.

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between solid copper and nitric acid is: Cu + 4HNO₃ → Cu(NO₃)₂ + 2NO₂ + 2H₂O Six mole ratios for this reaction are: 1. Cu : HNO₃ = \(\frac{1}{4}\) 2. Cu : Cu(NO₃)₂ = \(\frac{1}{1}\) 3. Cu : NO₂ = \(\frac{1}{2}\) 4. Cu : H₂O = \(\frac{1}{2}\) 5. HNO₃ : Cu(NO₃)₂ = \(\frac{4}{1}\) 6. HNO₃ : NO₂ = \(\frac{4}{2}\)

Step 1: Write the unbalanced chemical equation

Identify the reactants and products in the given reaction and write the unbalanced chemical equation for the reaction. Reactants: Solid copper (Cu) and nitric acid (HNO₃) Products: Copper(II) nitrate (Cu(NO₃)₂), nitrogen dioxide (NO₂), and water (H₂O) The unbalanced chemical equation is: Cu + HNO₃ → Cu(NO₃)₂ + NO₂ + H₂O

Step 2: Balance the chemical equation

Balance the atoms on both sides of the equation by adjusting the stoichiometric coefficients of the formulae appropriately. To balance the chemical equation, we follow these steps: 1. Balance elements other than hydrogen and oxygen (in this case, Cu and N). 2. Balance the oxygen atoms. 3. Balance the hydrogen atoms. The balanced chemical equation is: Cu + 4HNO₃ → Cu(NO₃)₂ + 2NO₂ + 2H₂O

Step 3: List the six mole ratios

To find the mole ratios, we will use the coefficients of the balanced chemical equation. There are four species involved in the reaction, and we can choose any of the reactants or products as a reference and form six mole ratios. The balanced chemical equation is: 1Cu + 4HNO₃ → 1Cu(NO₃)₂ + 2NO₂ + ２H₂O Mole ratios: 1. Mole ratio of Cu to HNO₃: \(\frac{1}{4}\) (Cu : HNO₃) 2. Mole ratio of Cu to Cu(NO₃)₂: \(\frac{1}{1}\) (Cu : Cu(NO₃)₂) 3. Mole ratio of Cu to NO₂: \(\frac{1}{2}\) (Cu : NO₂) 4. Mole ratio of Cu to H₂O: \(\frac{1}{2}\) (Cu : H₂O) 5. Mole ratio of HNO₃ to Cu(NO₃)₂: \(\frac{4}{1}\) (HNO₃ : Cu(NO₃)₂) 6. Mole ratio of HNO₃ to NO₂: \(\frac{4}{2}\) (HNO₃ : NO₂)

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. The term derives from the Greek words for 'element' and 'measure', which aptly describes its focus on the measurement of elements within a chemical equation.

In practice, stoichiometry allows chemists to predict the amounts of substances consumed and produced in a reaction. This is achieved by using the coefficients from a balanced chemical equation, which indicate the proportions in which substances react and are formed. For instance, in the balanced equation for copper reacting with nitric acid, the coefficient '4' before HNO₃ means that 4 moles of nitric acid react with 1 mole of copper.

Importance of Coefficients

The coefficients play a crucial role as they represent the mole ratio between the reactants and products. They are also essential for calculating the mass, volume, and number of particles involved in a chemical reaction.

Mole Ratio

The mole ratio is a critical concept in stoichiometry that defines the ratio of moles of one substance to the moles of another substance in a balanced chemical equation. It is a central idea for understanding how different substances interact and transform during chemical reactions.

Mole ratios are derived from the coefficients in a balanced chemical equation and are used to calculate how much of each reactant is needed to produce a desired amount of product. For the reaction of copper and nitric acid, the mole ratios give us essential information. For example, a mole ratio of \(\frac{1}{4}\) (Cu to HNO₃) tells us that for every mole of Cu used, four moles of HNO₃ are required.

Using Mole Ratios

Mole ratios are used to convert moles of one substance to moles of another. When performing calculations, it is important to set them up properly, keeping in mind that the mole ratio acts as a conversion factor that bridges two substances in a reaction.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and formation of chemical bonds. Each reaction is characterized by its reactants and products and can be depicted through a chemical equation. The equation provides a symbolic representation of the reaction, outlining the substances involved and their quantitative relation.

In the provided example, the reaction between copper and nitric acid is a typical chemical reaction where copper is oxidized, and nitrogen dioxide and water are formed alongside copper(II) nitrate. The chemical equation not only depicts the substances but also reflects the conservation of mass, stating that matter is neither created nor destroyed in a chemical reaction. This law is illustrated by the balanced equation where the number of atoms for each element is the same on both sides of the equation.

Categories of Chemical Reactions

There are various types of chemical reactions, such as synthesis, decomposition, single replacement, and double replacement. The reaction between copper and nitric acid is an example of a single replacement reaction, where one element replaces another in a compound.