On introduit 1 g d'eau dans un ballon de 2 litres où l'on...

On introduit $1 \mathrm{~g}$ d'eau dans un ballon de 2 litres où l'on avait préalablement fait le vide, fermé hermétiquement; la température ambiante est $22^{\circ} \mathrm{C}$. On chauffe ensuite le ballon, provoquant ainsi la vaporisation progressive de l'eau et l'augmentation de la pression. a) À quelle température l'eau sera-t-elle entièrement vaporisée ? Quelle sera alors la valeur de la pression? b) Le ballon est ensuite chauffé jusqu'à $110^{\circ} \mathrm{C}$, puis on le laisse refroidir. À quelle température la vapeur commencera-t-elle à se condenser ?

On introduit $1 \mathrm{~g}$ d'eau dans un ballon de 2 litres où l'on avait préalablement fait le vide, fermé hermétiquement; la température ambiante est $22^{\circ} \mathrm{C}$.
On chauffe ensuite le ballon, provoquant ainsi la vaporisation progressive de l'eau et l'augmentation de la pression.
a) À quelle température l'eau sera-t-elle entièrement vaporisée ? Quelle sera alors la valeur de la pression?
b) Le ballon est ensuite chauffé jusqu'à $110^{\circ} \mathrm{C}$, puis on le laisse refroidir. À quelle température la vapeur commencera-t-elle à se condenser ?

Key Concepts

Saturated Vapor Pressure

Saturated vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a specific temperature. It is a key parameter in determining the conditions under which a liquid will completely vaporize in a confined space, as well as when vapor will begin to condense upon cooling, independent of external pressure in a sealed container.

Closed System Thermodynamics

In a rigid, sealed container, the volume is fixed, meaning that the amount of water and space available for its vapor phase remain constant. The thermodynamic behavior of the water is governed by the interplay between its temperature and pressure under these constraints, influencing the phase transitions and determining the equilibria between liquid and vapor states.

Phase Equilibrium

This concept deals with the balanced state between two coexisting phases, such as liquid and vapor, where the rate of evaporation equals the rate of condensation. In a closed system at a given temperature, any disturbance in this balance leads the system back to equilibrium via changes in pressure or temperature, which is fundamental for understanding when complete vaporization or condensation begins.

Transcript

00:01 So in this example, we're told that we have a flask that has a volume of three times 10 to 3rd milliliters, which i went ahead and converted to meters cubed.

00:10 We're told that the initial temperature is 20 degrees celsius, which i went ahead and converted to kelvin.

00:16 And we're told it's at 1 atm, which i converted to pascal's.

00:19 So what happens is there's a stopper on this flask.

00:22 It's put into boiling water.

00:27 So we know that the temperature of boiling water is 373 .15 kelvin, and it's allowed to reach equilibrium.

00:36 So what they want to know is what the max pressure in the flask is.

00:41 All right.

00:42 So in order to find that, we need to find the initial number of moles.

00:46 So we're going to use our ideal gas law, which states that the pressure times the volume is equal to the number of moles times our ideal gas constant times the temperature.

00:54 We'll solve for n making n sub i being our initial number of moles it's going to be equal to the pressure times the volume in our case the initial pressure times the volume divided by our deal with gas constant that's the temperature or the initial temperature when we plug in for this we get that our initial number of moles is 1 or 0 .12 -4 -678 moles and then then we want to solve for the pressure, right, knowing our initial number of moles.

01:35 So the pressure is going to be equal to the initial number of moles times our ideal gas constant, times our final temperature because the temperature inside the flask increased when it was in the boiling water over the volume.

01:53 And this will give us our maximum pressure of 1 .289 times 10 to 5 pounds...

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