Electrode potential for Mg electrode varies according to the equation
`E_(Mg^(2+)//Mg)=E_(Mg^(2+)//Mg)^(Theta) -(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 regarding the electrode potential for the magnesium electrode and its graph, we can follow these steps:

### Step 1: Understand the Nernst Equation
The Nernst equation for the magnesium electrode is given as:
\[ E_{(Mg^{2+}//Mg)} = E_{(Mg^{2+}//Mg)}^{\Theta} - \frac{0.059}{2} \log \left(\frac{1}{[Mg^{2+}]}\right) \]
This can be rewritten as:
\[ E_{(Mg^{2+}//Mg)} = E_{(Mg^{2+}//Mg)}^{\Theta} + \frac{0.059}{2} \log [Mg^{2+}] \]
This shows that the electrode potential \(E\) is directly related to the logarithm of the concentration of \(Mg^{2+}\).

### Step 2: Identify the Variables
In the equation:
- \(E_{(Mg^{2+}//Mg)}\) is the electrode potential.
- \(E_{(Mg^{2+}//Mg)}^{\Theta}\) is the standard electrode potential.
- \(\log [Mg^{2+}]\) is the logarithm of the concentration of magnesium ions.

### Step 3: Identify the Form of the Equation
This equation can be expressed in the form of a straight line:
\[ y = mx + c \]
where:
- \(y\) is \(E_{(Mg^{2+}//Mg)}\)
- \(m\) is the slope, which is \(\frac{0.059}{2}\)
- \(x\) is \(\log [Mg^{2+}]\)
- \(c\) is the y-intercept, which is \(E_{(Mg^{2+}//Mg)}^{\Theta}\)

### Step 4: Determine the Graph Characteristics
Since the equation is linear:
- The slope \(m\) is positive (\(\frac{0.059}{2}\)), indicating that as \(\log [Mg^{2+}]\) increases, the electrode potential \(E_{(Mg^{2+}//Mg)}\) also increases.
- The graph will be a straight line with a positive slope.

### Step 5: Sketch the Graph
1. Draw the x-axis representing \(\log [Mg^{2+}]\).
2. Draw the y-axis representing \(E_{(Mg^{2+}//Mg)}\).
3. Plot the line starting from the y-intercept \(E_{(Mg^{2+}//Mg)}^{\Theta}\) and sloping upwards to the right.

### Conclusion
The graph of \(E_{(Mg^{2+}//Mg)}\) vs. \(\log [Mg^{2+}]\) is a straight line with a positive slope, indicating that an increase in the concentration of \(Mg^{2+}\) leads to an increase in the electrode potential.

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