What are the conditions for an ideal solution which obeys Raoult's law over the entire range of concentration ?

Options

A. `Delta_"mix"H=0, Delta_"mix"V=0, P_"Total"=p_A^(@)x_A+p_B^(@)x_B`
B. `Delta_"mix"H=+ve, Delta_"mix"V=0, P_"Total"=p_A^(@)x_A+p_B^(@)x_B`
C. `Delta_"mix"H=0, Delta_"mix"V=+ve, P_"Total"=p_A^(@)x_A+p_B^(@)x_B`
D. `Delta_"mix"H=0, Delta_"mix"V=0, P_"Total"=p_B^(@)x_B`

Explanation

To determine the conditions for an ideal solution that obeys Raoult's law over the entire range of concentration, we can break down the requirements step by step:

### Step 1: Understand Raoult's Law
Raoult's law states that the partial vapor pressure of each component in an ideal solution is directly proportional to its mole fraction in the solution. Mathematically, it can be expressed as:
\[ P_A = P_A^0 \cdot X_A \]
\[ P_B = P_B^0 \cdot X_B \]
where:
- \( P_A \) and \( P_B \) are the partial vapor pressures of components A and B,
- \( P_A^0 \) and \( P_B^0 \) are the vapor pressures of the pure components A and B,
- \( X_A \) and \( X_B \) are the mole fractions of components A and B in the solution.

### Step 2: Condition of Zero Heat of Mixing
For an ideal solution, the heat of mixing (\( \Delta H_{mix} \)) should be zero. This means that when the two components are mixed, there is no heat absorbed or released. This condition ensures that the interactions between the molecules of the different components are similar to those between the molecules of the same component.

### Step 3: Condition of Zero Volume Change
The volume change upon mixing (\( \Delta V_{mix} \)) should also be zero. This means that the total volume of the solution after mixing should be equal to the sum of the volumes of the individual components before mixing. This condition implies that there are no significant changes in the intermolecular spaces when the components are mixed.

### Step 4: Combine the Conditions
From the above conditions, we can summarize that for an ideal solution that obeys Raoult's law over the entire range of concentration:
1. The heat of mixing (\( \Delta H_{mix} \)) is zero.
2. The volume change upon mixing (\( \Delta V_{mix} \)) is zero.
3. The total vapor pressure of the solution can be calculated using the equation:
\[ P_{total} = P_A^0 \cdot X_A + P_B^0 \cdot X_B \]

### Conclusion
Thus, the conditions for an ideal solution that obeys Raoult's law over the entire range of concentration are:
- \( \Delta H_{mix} = 0 \)
- \( \Delta V_{mix} = 0 \)
- The total vapor pressure is given by \( P_{total} = P_A^0 \cdot X_A + P_B^0 \cdot X_B \)