Question

Explain why this chemical equation is not balanced and balance it if it can be balanced. \(\mathrm{Cr}^{2+}+\mathrm{Cl}_{2} \rightarrow \mathrm{Cr}^{3+}+2 \mathrm{Cl}^{-}\)

Short answer

The original equation was not balanced due to different charges. Balanced equation is: \(2 \mathrm{Cr}^{2+} + \mathrm{Cl}_{2} \rightarrow 2 \mathrm{Cr}^{3+} + 2 \mathrm{Cl}^{-}\).

Step-by-step solution

Understanding the Chemical Equation

The given chemical equation is \( \mathrm{Cr}^{2+} + \mathrm{Cl}_{2} \rightarrow \mathrm{Cr}^{3+} + 2 \mathrm{Cl}^{-} \). We need to ensure there are equal numbers of each kind of atom and charge on both sides of the reaction.

Analyze and Count Atoms and Charges

On the reactant side, there is 1 \(\mathrm{Cr}^{2+}\) ion and 1 \(\mathrm{Cl}_2\) molecule. Chlorine contains 2 chlorine atoms. On the product side, there is 1 \(\mathrm{Cr}^{3+}\) ion and 2 \(\mathrm{Cl}^-\) ions. Both sides have 2 chlorine atoms, so the atoms are balanced, but the charges are not.

Identify Imbalance in Charges

The total charge on the reactant side is \(+2\) from \(\mathrm{Cr}^{2+}\). On the product side, there is a total charge of \(+3\) from \(\mathrm{Cr}^{3+}\) and \(-2\) from 2 \(\mathrm{Cl}^{-}\), resulting in an overall charge of \(+1\). The charges are not balanced.

Adjust and Balance the Equation

To balance the charges, we can add more \(\mathrm{Cr}^{2+}\) ions on the reactant side. Use 2 \(\mathrm{Cr}^{2+}\) ions such that: \[2 \mathrm{Cr}^{2+} + \mathrm{Cl}_{2} \rightarrow 2 \mathrm{Cr}^{3+} + 2 \mathrm{Cl}^{-}\]. Now, the reactant side has a total charge of \(+4\) (from 2 \(\mathrm{Cr}^{2+}\)), and the product side also has \(+4\) (from 2 \(\mathrm{Cr}^{3+}\) and 2 \(\mathrm{Cl}^{-}\)). Both atom count and charges are balanced.

Key concepts

Stoichiometry

Stoichiometry is a fundamental part of chemistry that involves calculating the relationships between the quantities of reactants and products in chemical reactions. When balancing chemical equations, stoichiometry ensures that the number of atoms of each element is the same on both sides of the reaction. This concept is based on the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

When balancing the given chemical equation, we first count the number of each type of atom on both sides. Here:

• Chromium: 1 atom on each side initially
• Chlorine: 2 atoms on each side

While the chlorine atoms are equal, we need to ensure that every relevant particle, including ions, retains its stoichiometric balance by fully accounting for charge and particle count in both reactants and products.

By adding coefficients to the chemical equations, as seen in the step-by-step solution, stoichiometry helps achieve a balanced equation, reflecting the accurate quantitative needs for the complete reaction.

Oxidation States

Oxidation states refer to the degree of oxidation or reduction an atom has undergone in a molecule. This concept is crucial in redox reactions, where transfer of electrons occurs between chemical species during the reaction. In the provided problem, recognizing the change in oxidation states is essential to balance the equation.

Initially, chromium in \(\mathrm{Cr}^{2+}\) has an oxidation state of +2. After the reaction, it is converted to \(\mathrm{Cr}^{3+}\), indicating it has lost an electron, hence oxidized. Chlorine changes from a neutral molecule \(\mathrm{Cl}_{2}\) to \(\mathrm{Cl}^{-}\), where it gains electrons, indicating reduction.

Understanding these oxidation state changes is key to correctly deducing how many electrons are transferred and ensuring that both sides of the equation reflect a proper exchange, aiding in achieving a balanced chemical equation.

Charge Balance

Charge balance is an essential aspect of balancing chemical equations, particularly involving ionic species. A chemical equation is only considered balanced when not only the number of atoms but also the net charges on both sides are equivalent.

In the initial equation, the total charge on the left side is \(+2\) from \(\mathrm{Cr}^{2+}\) and on the right side, the combined charge is \(+1\) (\(+3\) from \(\mathrm{Cr}^{3+}\) and \(-2\) from two \(\mathrm{Cl}^{-}\) ions). This imbalance in charge indicates a need for adjustment.

To achieve charge balance, we ensure the total positive and negative charges are equal. By introducing more \(\mathrm{Cr}^{2+}\) ions, the calculation adjusts such that both sides have an identical charge of \(+4\), making this aspect of the chemical equation properly balanced. This careful consideration affirms the chemical equation aligns with both stoichiometric requirements and charge neutrality.