Which of the following is correct?

Options

A. `K_p` will always have some unit
B. `K_c` will always have some unit
C. `K_x` will never have any unit
D. When `trianglen=0, K_p=K_c=K_x`, then all the three Ks have the same unit

Answer

To solve the question regarding the correctness of statements related to equilibrium constants \( K_p \), \( K_c \), and \( K_x \), we will analyze the concepts step by step.

### Step 1: Understanding Equilibrium Constants
Equilibrium constants are used to express the ratio of the concentrations (or partial pressures) of products to reactants at equilibrium. The three types of equilibrium constants we are discussing are:
- \( K_p \): Equilibrium constant in terms of partial pressures.
- \( K_c \): Equilibrium constant in terms of concentrations.
- \( K_x \): Equilibrium constant in terms of mole fractions.

### Step 2: Relationship Between \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by the equation:
\[ K_p = K_c (RT)^{\Delta n} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in the number of moles of gas (moles of products - moles of reactants).

### Step 3: Analyzing \( \Delta n \)
- If \( \Delta n = 0 \): This means that the number of moles of gaseous products is equal to the number of moles of gaseous reactants. In this case, the equation simplifies to:
\[ K_p = K_c \]
This indicates that both \( K_p \) and \( K_c \) will have the same value and will be unitless.

- If \( \Delta n \neq 0 \): The units of \( K_p \) and \( K_c \) will differ, and they will not be unitless.

### Step 4: Conclusion on Units
- When \( \Delta n = 0 \), both \( K_p \) and \( K_c \) are unitless.
- When \( \Delta n \neq 0 \), \( K_p \) and \( K_c \) will have different units depending on the change in moles.

### Final Answer
Thus, the correct statement is that when \( \Delta n = 0 \), \( K_p \), \( K_c \), and \( K_x \) are all unitless and equal in magnitude.