Electrode potential for `Mg` electrode varies according to the equation
`E_(Mg^(2+)|Mg)=E_(Mg^(2+)|Mg)^(ϴ) -(0.059)/2 "log" 1/([Mg^(2+)])`
The graph of `E_(Mg^(2+)|Mg) vs log [Mg^(2+)]` is

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Explanation

To solve the question regarding the electrode potential for the magnesium electrode and its relationship with the concentration of \( \text{Mg}^{2+} \), we will follow these steps:

### Step 1: Understand the Nernst Equation
The Nernst equation for the magnesium electrode is given as:
\[ E_{(Mg^{2+}|Mg)} = E_{(Mg^{2+}|Mg)}^{\circ} - \frac{0.059}{2} \log \left( \frac{1}{[\text{Mg}^{2+}]} \right) \]
This can be rewritten as:
\[ E_{(Mg^{2+}|Mg)} = E_{(Mg^{2+}|Mg)}^{\circ} + \frac{0.059}{2} \log [\text{Mg}^{2+}] \]

### Step 2: Identify the Components of the Equation
In the equation:
- \( E_{(Mg^{2+}|Mg)} \) is the electrode potential.
- \( E_{(Mg^{2+}|Mg)}^{\circ} \) is the standard electrode potential.
- \( \frac{0.059}{2} \) is the slope of the line.
- \( \log [\text{Mg}^{2+}] \) is the logarithm of the concentration of magnesium ions.

### Step 3: Compare with the Linear Equation
The equation can be compared to the linear equation of the form:
\[ y = mx + c \]
Where:
- \( y \) corresponds to \( E_{(Mg^{2+}|Mg)} \)
- \( m \) (slope) is \( \frac{0.059}{2} \)
- \( x \) corresponds to \( \log [\text{Mg}^{2+}] \)
- \( c \) (y-intercept) is \( E_{(Mg^{2+}|Mg)}^{\circ} \)

### Step 4: Determine the Nature of the Graph
Since the equation is linear, the graph of \( E_{(Mg^{2+}|Mg)} \) versus \( \log [\text{Mg}^{2+}] \) will be a straight line. The slope will be positive because \( \frac{0.059}{2} \) is a positive value, indicating that as the concentration of \( \text{Mg}^{2+} \) increases (i.e., \( \log [\text{Mg}^{2+}] \) increases), the electrode potential \( E_{(Mg^{2+}|Mg)} \) also increases.

### Step 5: Conclusion
Thus, the graph of \( E_{(Mg^{2+}|Mg)} \) versus \( \log [\text{Mg}^{2+}] \) will be a straight line with a positive slope, starting from the y-intercept \( E_{(Mg^{2+}|Mg)}^{\circ} \).