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A mixture of liquids $A$ and $B$ exhibits ideal behavior. At $84^{\circ} \mathrm{C},$ the total vapor pressure of a solution containing 1.2 moles of $\mathrm{A}$ and 2.3 moles of $\mathrm{B}$ is $331 \mathrm{mmHg} .$ Upon the addition of another mole of B to the solution, the vapor pressure increases to $347 \mathrm{mmHg} .$ Calculate the vapor pressures of pure A and $B$ at $84^{\circ} \mathrm{C}$.

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$LDFs$

Chemistry 102

Chapter 12

Physical Properties of Solutions

Solutions

Carleton College

Brown University

Lectures

03:58

In chemistry, a solution is a homogeneous mixture composed of two or more substances. The term "solution" is also used to refer to the resultant mixture. The solution is usually a fluid. The particles of a solute are dispersed or dissolved in the solvent. The resulting solution is also called the solvent. The solvent is the continuous phase.

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In physics and thermodynamics, the natural tendency of a system to change its state is its tendency to increase the entropy of the system. It is a measure of the disorder in a system.

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all right for this question, We gotta set up a system of equations, and, um, we have two scenarios. Okay? The first scenario is before the addition off the extra beat in the second scenarios, when we add the extra beat. So for both cases, we can set up an equation for the total pressure. Okay, the total pressure off the system will be the pressure of eight. Plus the pressure of me came. Remember that for any, um uh, for any solution, the pressure, the Vape repression of one component that is volatile as the case of a B, they're both volatile will be the more fraction off that component I'm calling I in this case times the vapor pressure of that component when it's pure. So in this question, we're asked this. Were asked to find a vapor pressure off a when it's pure and be when it's pure. Okay, so let's rewrite the equation for the total pressure now, in terms off the molar fraction off a times the pressure off a pure molar. Fraction off the times the pressure off b pure. All right. Now all we have to do is to compute those more fractions for scenario one and scenario to so our scenario one. Let's compute the more a fresh Nall A We have 1.2 moles of eight. Okay, I'm gonna omit units for this question. Just for simplicity. Remember, this is mole, of course. And the total malls is 1.2 bluffs, 2.3, which is the number of most of beef. Okay, And this is approximately 0.34. Okay, you don't have to come do the same for B, because the smaller fraction when you add up, the more fractions you have to get one. Right? So the more refraction off B is just one minus this, which is 0.66 Okay, All right. So that will allow us to set up the first equation. So we know that before the addition of extra be the pressure of the system is 331 the vapor pressure of the solution looking millimeters millimeters of mercury. But I'm gonna I'm gonna meet the unit. You okay? Ah, what else? So I'm looking up at this equation right here. So now we have the more fractions, so let's substitute that. So 0.34 pressure of a plus 0.66 Pressure will be okay. Now, first in there, you to we add extra B to the system. So now the Mueller fraction with off A It's 1.2 divided by 1.2 plus 2.3 plus one extra mole of beef. I came and there will be 0.27 Which means that the molar fractional B is just a complement of this. 0.73 Okay, uh, so we can set up the other equation and there will be, Let's see, the total pressure will be 347 Now we have 0.27 for eight and we have 0734 b Who that's it. This is one equation. This is this another equation? So we have two equations, two variables. You can solve this by this standard techniques that you learning mathematics to do this and you should find the vapor pressure of a is approximately 1 80 millimeters of mercury. And the pressure of being pure B is for all nine. All right,

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