Three metals, A, B and C, with solutions of their respective cations are tested in a voltaic cell with the following results:
A and B: A is the cathode
B and C: C is the cathode
A and C : A is the anode
What is the order of reduction potentials from highest to lowest for the cations of these metals?

Options

A. A gt B gtC
B. B gt C gtA
C. C gt A gt B
D. B gt A gtC

Answer

To determine the order of reduction potentials from highest to lowest for the cations of metals A, B, and C based on the given information, we can analyze the results of the voltaic cell tests step by step.

### Step 1: Analyze the Results of the Tests
1. **Test 1: A and B - A is the cathode**
- In this case, A has a higher reduction potential than B because the cathode is where reduction occurs. Therefore, we can write:
\[ E^\circ_A > E^\circ_B \]

2. **Test 2: B and C - C is the cathode**
- Here, C has a higher reduction potential than B. Thus, we can write:
\[ E^\circ_C > E^\circ_B \]

3. **Test 3: A and C - A is the anode**
- In this test, A is the anode, which means it has a lower reduction potential than C. Therefore, we can write:
\[ E^\circ_A < E^\circ_C \]

### Step 2: Combine the Inequalities
From the three tests, we have the following inequalities:
1. From Test 1: \( E^\circ_A > E^\circ_B \)
2. From Test 2: \( E^\circ_C > E^\circ_B \)
3. From Test 3: \( E^\circ_A < E^\circ_C \)

### Step 3: Order the Reduction Potentials
Now, we can combine these inequalities to find the order of the reduction potentials:
- From \( E^\circ_A < E^\circ_C \) and \( E^\circ_A > E^\circ_B \), we can conclude that:
\[ E^\circ_C > E^\circ_A > E^\circ_B \]

### Final Order of Reduction Potentials
Thus, the order of reduction potentials from highest to lowest is:
\[ E^\circ_C > E^\circ_A > E^\circ_B \]

### Summary
- **Highest Reduction Potential:** C
- **Middle Reduction Potential:** A
- **Lowest Reduction Potential:** B