What reaction can occur, if any, when the following experiments are carried out under standard-state conditions? (a) Oxygen gas is bubbled through an acidic solution of Cr(NO3)3.

Verified step by step guidance

1. Identify the oxidation states of the elements involved in the reaction. Chromium in Cr(NO_3)_3 is in the +3 oxidation state, and oxygen gas (O_2) is in the 0 oxidation state.
2. Determine the possible redox reactions. In acidic solutions, oxygen can act as an oxidizing agent. Consider the standard reduction potentials to see if oxygen can oxidize Cr^3+ to a higher oxidation state.
3. Consult a table of standard reduction potentials. The half-reaction for the reduction of O_2 in acidic solution is O_2 + 4H^+ + 4e^- \rightarrow 2H_2O with a standard potential of +1.23 V. Chromium can be oxidized from Cr^3+ to Cr_2O_7^{2-} in acidic solution: 2Cr^3+ + 7H_2O \rightarrow Cr_2O_7^{2-} + 14H^+ + 6e^- with a standard potential of -1.33 V.
4. Calculate the cell potential for the reaction. The overall cell potential is the difference between the reduction potential of the oxidizing agent and the oxidation potential of the reducing agent. If the cell potential is positive, the reaction is spontaneous under standard conditions.
5. Conclude whether a reaction occurs. If the calculated cell potential is positive, oxygen can oxidize Cr^3+ to Cr_2O_7^{2-} in acidic solution, indicating a spontaneous reaction.

Key Concepts

Redox Reactions

Redox reactions involve the transfer of electrons between species, resulting in changes in oxidation states. In the context of the question, oxygen gas can act as an oxidizing agent, potentially oxidizing chromium in Cr(NO3)3 from a lower oxidation state to a higher one, which is crucial for predicting the reaction outcome.

Acidic Solutions

An acidic solution has a pH less than 7 and contains a higher concentration of hydrogen ions (H+). The presence of an acid can influence the solubility and reactivity of metal ions, such as chromium, and can facilitate redox reactions by providing protons that may participate in the reaction mechanism.

Standard-State Conditions

Standard-state conditions refer to a set of specific conditions (1 atm pressure, 25°C temperature, and 1 M concentration for solutions) under which thermodynamic data is measured. Understanding these conditions is essential for predicting the feasibility and direction of chemical reactions, as they provide a baseline for comparing reaction energies and equilibria.