Answer
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Hint: Find the total pressure using the formula $P_{total}=X_A \cdot \dot{P}_{A}+ X_B \cdot \dot{P}_{B}$. Then we can find the mole fraction.
Complete step by step answer:
Let us find the $P_{total}$ by using the formula $P_{total}=X_A \cdot \dot{P}_{A}+ X_B \cdot \dot{P}_{B}$
Where $\dot{P}_{A}$ is the is the partial pressures of A and $\dot{P}_{B}$ is the is the partial pressures of B.
And $X_A$ is the mole fraction of A and $X_B$ is the mole fraction of B
$P_{total}=0.5 \times 400+ 0.5\times 600$
By solving we get,
$P_{total}$=50 mm Hg
Now, we can find mole fraction of A in vapour,
$Y_A= \dfrac{P_A}{ P_{total}}= \dfrac{0.5 \times 400}{500}=0.4$
Additional information:
The pressure exerted by a vapor in equilibrium with the condensed phases at a given temperature in a closed system is called the vapour pressure.
$P_{total}=X_A \cdot \dot{P}_{A}+ X_B \cdot \dot{P}_{B}$ equation is also known as Dalton’s law of partial pressure.
Note: In these types of questions sometimes $X_B$ may not be given. We can find $X_B$ by $X_B=1-X_A$
Complete step by step answer:
Let us find the $P_{total}$ by using the formula $P_{total}=X_A \cdot \dot{P}_{A}+ X_B \cdot \dot{P}_{B}$
Where $\dot{P}_{A}$ is the is the partial pressures of A and $\dot{P}_{B}$ is the is the partial pressures of B.
And $X_A$ is the mole fraction of A and $X_B$ is the mole fraction of B
$P_{total}=0.5 \times 400+ 0.5\times 600$
By solving we get,
$P_{total}$=50 mm Hg
Now, we can find mole fraction of A in vapour,
$Y_A= \dfrac{P_A}{ P_{total}}= \dfrac{0.5 \times 400}{500}=0.4$
Additional information:
The pressure exerted by a vapor in equilibrium with the condensed phases at a given temperature in a closed system is called the vapour pressure.
$P_{total}=X_A \cdot \dot{P}_{A}+ X_B \cdot \dot{P}_{B}$ equation is also known as Dalton’s law of partial pressure.
Note: In these types of questions sometimes $X_B$ may not be given. We can find $X_B$ by $X_B=1-X_A$
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