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P(A)and P(B) are the vapour pressure of ...

`P_(A)and P_(B)` are the vapour pressure of pure liquid components ,Aand B respectively of an ideal binary solution,If `x_(A)` represents the mole fraction of component A, the total pressure of the solution will be

A

`p_(A)+chi_(A)(p_(B)-p_(A))`

B

`p_(A)+chi_(A)(chi_(A)-p_(B))`

C

`p_(B)+chi_(A)(p_(B)-p_(A))`

D

`p_(B)+chi_(A)(p_(A)-p_(B))`

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To find the total pressure of an ideal binary solution consisting of components A and B, we can follow these steps: ### Step-by-Step Solution: 1. **Identify Given Values**: - Let \( P_A \) be the vapor pressure of pure component A. - Let \( P_B \) be the vapor pressure of pure component B. - Let \( x_A \) be the mole fraction of component A in the solution. - The mole fraction of component B, \( x_B \), can be expressed as \( x_B = 1 - x_A \). 2. **Apply Raoult's Law**: - According to Raoult's Law, the partial vapor pressure of each component in the solution is given by: - Partial vapor pressure of A: \( P_A' = x_A \cdot P_A \) - Partial vapor pressure of B: \( P_B' = x_B \cdot P_B = (1 - x_A) \cdot P_B \) 3. **Calculate Total Pressure**: - The total pressure \( P_{total} \) of the solution is the sum of the partial pressures: \[ P_{total} = P_A' + P_B' = x_A \cdot P_A + (1 - x_A) \cdot P_B \] 4. **Simplify the Expression**: - Expanding the equation: \[ P_{total} = x_A \cdot P_A + P_B - x_A \cdot P_B \] - Rearranging the terms gives: \[ P_{total} = P_B + x_A \cdot (P_A - P_B) \] 5. **Final Expression**: - Thus, the total pressure of the solution can be expressed as: \[ P_{total} = P_B + x_A \cdot (P_A - P_B) \] ### Conclusion: The total pressure of the ideal binary solution is given by: \[ P_{total} = P_B + x_A \cdot (P_A - P_B) \]
To find the total pressure of an ideal binary solution consisting of components A and B, we can follow these steps: ### Step-by-Step Solution: 1. **Identify Given Values**: - Let \( P_A \) be the vapor pressure of pure component A. - Let \( P_B \) be the vapor pressure of pure component B. - Let \( x_A \) be the mole fraction of component A in the solution. ...
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