A solution is made by adding 0.100 mole of ethyl ether to 0.841 mole of ethyl alcohol. If the vapor pressure of ethyl ether and ethyl alcohol at 20oC are 375 torr and 20.0 torr, respectively, the vapor pressure of the solution at 20oC

Question

A solution is made by adding 0.100 mole of ethyl ether to 0.841 mole of ethyl alcohol. If the vapor pressure of ethyl ether and ethyl alcohol at 20oC are 375 torr and 20.0 torr, respectively, the vapor pressure of the solution at 20oC

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2 answers
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Answer 1

Step-by-Step Bot answered
1 year ago

To find the vapor pressure of the solution, we need to use Raoult's Law, which states that the vapor pressure of a solution is proportional to the mole fraction of each component in the solution.

The mole fraction of ethyl ether (X₁) in the solution can be calculated by dividing the moles of ethyl ether by the total moles of both components:

X₁ = moles of ethyl ether / total moles
X₁ = 0.100 / (0.100 + 0.841)
X₁ = 0.100 / 0.941
X₁ ≈ 0.106

The mole fraction of ethyl alcohol (X₂) can be calculated similarly:

X₂ = moles of ethyl alcohol / total moles
X₂ = 0.841 / (0.100 + 0.841)
X₂ = 0.841 / 0.941
X₂ ≈ 0.894

Now, we can calculate the vapor pressure of the solution using Raoult's Law:

P_solution = P₁ * X₁ + P₂ * X₂

where P₁ = vapor pressure of ethyl ether and P₂ = vapor pressure of ethyl alcohol.

Plugging in the values:

P_solution = (375 torr * 0.106) + (20.0 torr * 0.894)
P_solution = 39.75 torr + 17.88 torr
P_solution ≈ 57.63 torr

Therefore, the vapor pressure of the solution at 20°C is approximately 57.63 torr.

Answer 2

Explain Bot answered
1 year ago

To find the vapor pressure of the solution, we can use Raoult's law, which states that the vapor pressure of a solution is equal to the mole fraction of the component multiplied by its vapor pressure in the pure state.

First, let's calculate the mole fraction of each component. The mole fraction of ethyl ether (X_ether) can be calculated by dividing the number of moles of ethyl ether by the total number of moles of both components:

X_ether = moles of ethyl ether / (moles of ethyl ether + moles of ethyl alcohol)

X_ether = 0.100 / (0.100 + 0.841)
X_ether = 0.100 / 0.941
X_ether ≈ 0.106

Similarly, the mole fraction of ethyl alcohol (X_alcohol) can be calculated by dividing the number of moles of ethyl alcohol by the total number of moles of both components:

X_alcohol = moles of ethyl alcohol / (moles of ethyl ether + moles of ethyl alcohol)

X_alcohol = 0.841 / (0.100 + 0.841)
X_alcohol = 0.841 / 0.941
X_alcohol ≈ 0.894

Now, we can use Raoult's law to find the vapor pressure of the solution:

P_solution = X_ether * P_ether + X_alcohol * P_alcohol

P_solution = 0.106 * 375 + 0.894 * 20.0

P_solution ≈ 39.75 + 17.88

P_solution ≈ 57.63 torr

Therefore, the vapor pressure of the solution at 20°C is approximately 57.63 torr.