The incorrect expression among the following is

Options

A. `(DeltaG_("system"))/(DeltaG_("total"))=-T`
B. in isothermal process, `W_("reversible")=-nRT"in"(V_(f))/(V_(i))`
C. In `K=(DeltaH-TDeltaS^(@))/(RT)`
D. `K=e^(-DeltaG^(@)//RT)`

Explanation

To determine the incorrect expression among the given options, we will analyze each expression step by step.

### Step 1: Analyze the First Expression
The first expression states:
\[ \frac{\Delta G}{\Delta S_{total}} = -T \]
Using the Gibbs Helmholtz equation, we know that:
\[ \Delta G = \Delta H - T \Delta S \]
For a system where the total entropy change is considered, if \(\Delta H_{total} = 0\), then:
\[ \Delta G = -T \Delta S_{total} \]
Thus, the first expression is correct.

**Hint:** Review the Gibbs Helmholtz equation and the definition of total entropy change.

### Step 2: Analyze the Second Expression
The second expression relates to an isothermal reversible process:
\[ \Delta U = Q + W \]
In an isothermal process for an ideal gas, the change in internal energy (\(\Delta U\)) is zero. Therefore:
\[ 0 = Q + W \]
For reversible work done, we have:
\[ W = -Q \]
This leads to:
\[ W = -nRT \ln\left(\frac{V_{final}}{V_{initial}}\right) \]
This expression is also correct.

**Hint:** Recall the first law of thermodynamics and the characteristics of isothermal processes.

### Step 3: Analyze the Third Expression
The third expression states:
\[ \Delta G^0 = \Delta H^0 - T \Delta S^0 \]
This is correct, and we also have:
\[ \Delta G^0 = -RT \ln K \]
Rearranging gives:
\[ \ln K = -\frac{\Delta G^0}{RT} \]
If we substitute \(\Delta G^0\) in the expression, we would get:
\[ \Delta H^0 - T \Delta S^0 = -RT \ln K \]
This expression is also correct.

**Hint:** Understand the relationships between Gibbs free energy, enthalpy, and entropy.

### Step 4: Analyze the Fourth Expression
The fourth expression states:
\[ \Delta G^0 = -RT \ln K \]
From this, we can derive:
\[ \ln K = -\frac{\Delta G^0}{RT} \]
When expressed in exponential form:
\[ K = e^{-\frac{\Delta G^0}{RT}} \]
This expression is also correct.

**Hint:** Familiarize yourself with the relationship between Gibbs free energy and equilibrium constant.

### Conclusion
After analyzing all the expressions, it becomes clear that the incorrect expression is the second one.

Thus, the final answer is:
**The incorrect expression is the second option.**