Question

The ion \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) is weakly acidic. Write an equation showing its behavior as a Brønsted-Lowry acid in water.

Short answer

The chemical equation representing the behavior of the ion \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) as a Brønsted-Lowry acid in water is \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\mathrm{OH}^{2+} + \mathrm{H}_{3}\mathrm{O}^{+}\).

Step-by-step solution

Understand Brønsted-Lowry Acid Concept

Recognize that according to Brønsted-Lowry theory, an acid is a substance that can donate a proton (H+ ion). In the given ion, \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\), the proton donor will be one of the water molecules attached to the chromium ion.

Write the Ion Before Reaction

Start with the complex ion before it has acted as an acid: \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\).

Write the Reaction with Water

Present the acid-base reaction with water: \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\) donates a proton to a water molecule to form the hydronium ion \(\mathrm{H}_{3}\mathrm{O}^{+}\) and a \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\mathrm{OH}^{2+}\) ion.

Write the Balanced Chemical Equation

Combine the reactants and products to form the balanced chemical equation: \(\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\mathrm{OH}^{2+} + \mathrm{H}_{3}\mathrm{O}^{+}\).

Key concepts

Acid-Base Reactions

In chemistry, acid-base reactions are essential for understanding how substances interact within various environments, playing a crucial role in both natural processes and industrial applications. In a typical acid-base reaction, an acid reacts with a base to form a salt and usually water in a process called neutralization. However, according to the Brønsted-Lowry acid theory, it is characterized more broadly, focusing on the transfer of protons.

A Brønsted-Lowry acid, like the chromium complex ion \texttt{Cr}\(\texttt{H}_{2}\texttt{O}\)_{6}^{3+}, is defined as a proton donor. The reaction of this complex ion with water sheds light on its weakly acidic nature, as it donates a proton to a water molecule leading to the formation of new products that include the hydronium ion \texttt{H}_{3}\texttt{O}^{+}, a clear indictor of acidity in an aqueous solution.

Proton Donation

Proton donation is the hallmark of the Brønsted-Lowry theory of acids and bases. It turns the spotlight on the exchange of a single proton (\texttt{H}^{+}) between molecules. When an acid donates a proton, it transforms into its conjugate base, which has the potential to accept a proton. Similarly, when a base receives a proton, it becomes its conjugate acid.

In the example of the chromium complex ion \texttt{Cr}\(\texttt{H}_{2}\texttt{O}\)_{6}^{3+}, one of the water molecules bound to the chromium ion loses a hydrogen atom as a proton (\texttt{H}^{+}). This process leaves us with a hydroxide group (\texttt{OH}^{-}) that remains associated with the chromium, creating a \texttt{Cr}\(\texttt{H}_{2}\texttt{O}\)_{5}\texttt{OH}^{2+} complex, illustrating the act of proton donation.

Chemical Equilibrium

Chemical equilibrium refers to a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentration of reactants and products over time. It is a dynamic balance, not a static one, as the reactions continue to occur in both directions concurrently.

In the context of the chromium complex ion acting as a Brønsted-Lowry acid, the established equilibrium would involve the original complex ion, the water molecules, the protonated form of water (Hydronium ion), and the new chromium complex formed after proton donation. Understanding the position of equilibrium gives us insight into the acid's strength; in this case, the weak acidity of the chromium complex is indicated by the equilibrium favoring the reactants slightly more than the products.

Complex Ions

Complex ions are ions comprising a metal ion at their center surrounded by various molecules or ions, called ligands, which bond to the central ion. These complex ions can display a wide range of chemical behaviors depending on the nature of the central ion and its ligands.

The chromium complex ion, \texttt{Cr}\(\texttt{H}_{2}\texttt{O}\)_{6}^{3+}, comprises a chromium ion surrounded by six water molecules acting as ligands. The behavior of these complex ions in acid-base reactions relies on the ability of the water molecules, in this case, to act as Brønsted-Lowry acids by donating protons. By changing the nature of the ligands or the metal ion, the acidity or basicity of complex ions can be drastically altered, influencing their reactivity and the outcome of acid-base reactions they participate in.