Liquid A has vapor pressure x, and liquid B has vapor...

Liquid A has vapor pressure $x,$ and liquid B has vapor pressure y. What is the mole fraction of the liquid mixture if the vapor above the solution is $30 . \%$ A by moles? $50 . \%$ A? $80 . \%$ A? (Calculate in terms of $x$ and $y .$ ) Liquid A has vapor pressure $x,$ liquid $\mathrm{B}$ has vapor pressure y. What is the mole fraction of the vapor above the solution if the liquid mixture is $30 . \%$ A by moles? $50 . \%$ A? $80 . \%$ A? (Calculate in terms of $x$ and $y .$ )

Transcript

00:01 Hello, here the liquid a is mixed with liquid b, and we have to calculate more fraction of the liquid a in the mixture if the pressure of vapors a is 30 % of total pressure by mole.

00:18 So here we are giving vapor pressure of the pure liquids a and b, which are x and y.

00:26 And now let's consider, yeah, let's look at the overall pressure which is created by these two liquids.

00:33 So the total pressure created by these two liquids equals to the summary pressure, some of the pressure created by liquid a and by liquid b.

00:42 And this is in turn pressure of liquid a equals to the mole fraction of liquid a times its vapor pressure of pure a vapors, which is x.

00:56 And same as for liquid b, so it equals to a small fraction of liquid b, tires, vapor pressure of pure liquid b, which is y.

01:07 And here we can substitute, yeah, we know that the sum of c, c, a, and c b is 1.

01:16 Therefore, we end up with this expression.

01:19 So now we know that in question a, 30 % of total pressure is by liquid a.

01:25 Therefore, pa equals to 0 .3 point p.

01:31 And we also know that pa equals to xxxa times pa.

01:36 So now we can, now what we do, we substitute in this equation, we substitute pa with this formula, and we substitute total pressure, let's label it with red color with this formula.

02:04 So therefore it results in the following.

02:09 So for the first case, for the first case, it's ca times pa, which is x equals to 0 .3 times pa not, plus 1 minus xca times pb not.

02:32 So let's substitute now p .a .0 with x and p b not with y.

02:44 So what are we getting? ca equal, sorry, c .a times x equals to, so here we have to open the brackets.

02:58 So it's 0 .3, c .a.

03:01 Pa, not which is x.

03:07 Plus 0 .3y, which is pb0 minus 0 .3y xca.

03:21 Now let's group everything with xca on the right part of this equation.

03:34 So therefore xxia times x minus 0 .3 xxia x minus 0 .3 xa x plus 0 .3 x .a y equals to 0 .3y.

03:51 So therefore, 0 .7 xa x plus 0 .3 c .y equals to 0 .3y...

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