K' is Henry's constant and has the unit

Options

A. atm `mol^(-1)dm^(3)`
B. `mol^(-1)dm^(3)atm^(-1)`
C. atm mol `dm^(-3)`
D. mol `dm^(-3) atm^(-1)`

Explanation

To determine the unit of Henry's constant (K'), we can follow these steps:

### Step 1: Understand Henry's Law
Henry's Law states that the partial pressure of a gas (P) is directly proportional to the mole fraction (X) of the gas in a solution. This can be expressed mathematically as:
\[ P = K_H \cdot X \]
where \( K_H \) is Henry's constant.

### Step 2: Rearranging the Equation
We can rearrange the equation to express Henry's constant:
\[ K_H = \frac{P}{X} \]

### Step 3: Identify the Units
- **Partial Pressure (P)**: The unit of pressure is typically expressed in atmospheres (atm).
- **Mole Fraction (X)**: The mole fraction is a dimensionless quantity, as it is the ratio of the number of moles of the gas to the total number of moles in the solution.

### Step 4: Substitute the Units into the Equation
Now, substituting the units into the equation for Henry's constant:
\[ K_H = \frac{\text{atm}}{\text{dimensionless}} \]
This simplifies to:
\[ K_H = \text{atm} \]

### Step 5: Relate to Solubility
Alternatively, we can express Henry's law in terms of solubility (C) and relate it to pressure:
\[ C = K_H \cdot P \]
Where:
- **Solubility (C)**: The unit of solubility is moles per liter (mol/L), which can also be expressed as moles per cubic decimeter (mol/dm³).

### Step 6: Rearranging for K_H
Rearranging gives:
\[ K_H = \frac{C}{P} \]

### Step 7: Substitute the Units Again
Substituting the units for solubility and pressure:
- Solubility (C) = mol/dm³
- Partial Pressure (P) = atm

Thus:
\[ K_H = \frac{\text{mol/dm}^3}{\text{atm}} \]
This can be expressed as:
\[ K_H = \text{mol} \cdot \text{dm}^{-3} \cdot \text{atm}^{-1} \]

### Final Answer
The unit of Henry's constant (K') is:
\[ \text{mol} \cdot \text{dm}^{-3} \cdot \text{atm}^{-1} \]

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