Question

Heating causes the copper mineral malachite, \(\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2}\), wo decompose. Write a balanced equation for the reaction.

Short answer

The balanced equation for the decomposition of malachite when heated is \(2\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2} \rightarrow 4\mathrm{CuO} + 2\mathrm{H}_{2}\mathrm{O} + 2\mathrm{CO}_{2}\).

Step-by-step solution

- Identify the Initial Compound and Products

The initial copper mineral referred to is malachite, which has the formula \(\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2}\). When heated, it decomposes into several products. For balancing the equation, the exact products need to be known. In this case, the products are Copper (II) Oxide (CuO), Water (H2O) and Carbon Dioxide (CO2). So initially, the unbalanced equation looks like this: \(\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2} \rightarrow \mathrm{CuO} + \mathrm{H}_{2}\mathrm{O} + \mathrm{CO}_{2}\)

- Balancing the Equation

The next step is to balance this equation. Balancing starts with counting the number of atoms for each element on both sides. It is also important to remember that the number of atoms for each element should be the same on both sides of the equation. The equation becomes: \(2\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2} \rightarrow 4\mathrm{CuO} + 2\mathrm{H}_{2}\mathrm{O} + 2\mathrm{CO}_{2}\)

- Verifying that the equation is balanced

To ensure that this equation is correctly balanced, one must again count and compare the number of atoms present in each element on both the left and right side of the equation. If the numbers match for all elements, the equation is accurately balanced.

Key concepts

Chemical Decomposition

Chemical decomposition, also known as chemical breakdown, is a fundamental type of chemical reaction where a compound is broken down into two or more simpler substances. This usually occurs under specific conditions, such as high temperature, the presence of a catalyst, or electricity.

For example, when malachite, a copper carbonate hydroxide mineral, undergoes decomposition due to heat, it breaks down into copper(II) oxide, water, and carbon dioxide. The general form of a decomposition reaction is \[AB \rightarrow A + B\], where \(AB\) is the decomposing compound. Understanding the products of decomposition is crucial when attempting to balance the chemical equation of this reaction.

Chemical Reaction

A chemical reaction involves the transformation of one set of chemical substances into another. Reactants are substances that start a reaction, and the resulting substances are called products.

During a reaction, reactant bonds are broken, and new bonds form to create the products. The law of conservation of mass dictates that the mass of the reactants must equal the mass of the products; thus, the number of atoms of each element must remain the same before and after the reaction. This principle is the foundation for balancing chemical equations, ensuring that mass and charge are maintained throughout the reaction.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. The core principle of stoichiometry is the conservation of mass and the concept of the mole, a unit that measures the amount of substance.

To apply stoichiometry to balance equations, one must equalize the number of atoms for each element on both sides of the equation, as seen in the step-by-step solution for the decomposition of malachite. In balancing, coefficients are added in front of the compounds to adjust the atoms' quantity without changing the actual nature of the substances involved. These coefficients later help in determining the proportional relationships in a reaction, essential for various calculations, such as determining yield or converting units.

Malachite Decomposition

The decomposition of malachite, a bright green mineral consisting of copper carbonate hydroxide \(\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2}\), exemplifies a chemical decomposition reaction. When malachite is heated, it breaks down into copper(II) oxide (CuO), water (H2O), and carbon dioxide (CO2).

To correctly capture this transformation, the initial unbalanced reaction is represented as \[\mathrm{CuCO}_{3}-\mathrm{Cu}(\mathrm{OH})_{2} \rightarrow \mathrm{CuO} + \mathrm{H}_{2}\mathrm{O} + \mathrm{CO}_{2}\]. Then, we balance the chemical equation by altering the coefficients, ensuring the same number of each type of atom on both sides. This process helps us understand the molar ratios of the reactants and products, which is crucial for further stoichiometric calculations and practical applications in chemistry.