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 problem, we need to analyze the given equation for the electrode potential of the magnesium electrode and determine the nature of the graph of \( E_{Mg^{2+}|Mg} \) versus \( \log [Mg^{2+}] \).

### Step-by-Step Solution:

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

2. **Identifying the Variables**:
In this equation, we can identify:
- \( E \) (the electrode potential) corresponds to \( E_{Mg^{2+}|Mg} \)
- \( \log [Mg^{2+}] \) is the independent variable (let's denote it as \( x \))
- The slope \( m \) of the line is \( \frac{0.059}{2} \)
- The y-intercept \( c \) is \( E_{Mg^{2+}|Mg}^{\circ} \)

3. **Formulating the Linear Equation**:
The equation can be expressed in the form of a linear equation \( y = mx + c \):
\[ E = \frac{0.059}{2} \log [Mg^{2+}] + E_{Mg^{2+}|Mg}^{\circ} \]
Here, \( y \) is \( E \), \( m \) is \( \frac{0.059}{2} \), \( x \) is \( \log [Mg^{2+}] \), and \( c \) is \( E_{Mg^{2+}|Mg}^{\circ} \).

4. **Graph Characteristics**:
- The graph of \( E \) versus \( \log [Mg^{2+}] \) will be a straight line.
- The slope of the line is positive since \( \frac{0.059}{2} \) is a positive value.
- The y-intercept will be at \( E_{Mg^{2+}|Mg}^{\circ} \).

5. **Conclusion**:
Therefore, the graph of \( E_{Mg^{2+}|Mg} \) versus \( \log [Mg^{2+}] \) is a straight line with a positive slope.