Porous pellets of TiO₂ can be reduced to titanium metal at the cathode of an electrochemical cell containing molten CaCl₂ as the electrolyte. When the TiO₂ is reduced, the O^2-ions dis-solve in the CaCl₂ and are subsequently oxidized to O₂ gas at the anode. This approach may be the basis for a less expensive process than the one currently used for producing titanium.
(c) Write balanced equations for the anode, cathode, and overall cell reactions.

검증된 단계별 안내

insert step 1> Identify the half-reactions occurring at the cathode and anode. At the cathode, TiO_2 is reduced to titanium metal, and at the anode, O^{2-} ions are oxidized to O_2 gas.

insert step 2> Write the reduction half-reaction at the cathode. TiO_2 is reduced to Ti metal, so the half-reaction is: TiO_2 + 4e^- + 4H^+ \(\rightarrow\) Ti + 2H_2O.

insert step 3> Write the oxidation half-reaction at the anode. O^{2-} ions are oxidized to O_2 gas, so the half-reaction is: 2O^{2-} \(\rightarrow\) O_2 + 4e^-.

insert step 4> Balance the electrons in both half-reactions to ensure the number of electrons lost in the oxidation reaction equals the number gained in the reduction reaction.

insert step 5> Combine the balanced half-reactions to write the overall balanced cell reaction.

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주요 개념

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Electrochemical Cells

Electrochemical cells are devices that convert chemical energy into electrical energy through redox reactions. They consist of two electrodes: the anode, where oxidation occurs, and the cathode, where reduction takes place. Understanding the flow of electrons and the movement of ions in these cells is crucial for writing balanced equations for the reactions involved.

Oxidation and Reduction

Oxidation and reduction are fundamental concepts in chemistry that describe the transfer of electrons between species. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. In the context of the electrochemical cell described, the TiO2 is reduced at the cathode, and the O2- ions are oxidized at the anode, which is essential for balancing the overall cell reaction.

Balancing Redox Reactions

Balancing redox reactions requires ensuring that the number of electrons lost in oxidation equals the number gained in reduction. This involves identifying the oxidation states of the elements involved and adjusting coefficients in the half-reactions to achieve mass and charge balance. Mastery of this concept is necessary to write accurate balanced equations for the anode, cathode, and overall reactions in the electrochemical cell.