Carbon tetrachloride (CCl4) and benzene (C6H6) form ideal solutions. Consider an equimolar solution of CCl4 and C6H6 at 25°C. The vapor above this solutionis collected and condensed. Using the following data, determine the composition in mole fraction of the condensed vapor.
You didn't furnish any data.
If they are equimolar, then
XCCl4 = 0.5 and
XC6H6 = 0.5
Then partial pressure CCl4 = XCCl4 x PoCCl4 and
partial pressure C6H6 = XC6H6 x PoC6H6
Total P = partial pressure CCl4 + partial pressure C6H6.
XCCl4 in the vapor = PCCl4/total P.
XC6H6 in the vapor = PC6H6/total P.
This will be the composition on condensation.
To solve the problem, you need to find the relative vapor pressures for the two species. Since you're given the delta g values you can calculate the delta g for the reaction of the liquid going to vapor
C6H6(l)->C6H6(g)
Delta g= 129.66-124.5= 5.16
Do the same for CCl4 you'll get 4.62
Then use delta g= -RTln(K)
And solve for K
For example, for C6H6
5160=-8.314*298*ln(k)
K= .125
Do same for CCl4 and you'll get
K= 0.155
Since k indicates how much each reaction is going to the right, it is proportional to vapor pressure. Therefore, the relative vapor pressure of CCl4 to C6H6 is K(CCl4)/K(C6H6)= 0.155/0.125=1.24
So when vapor pressure C6H6 is 1, the vapor pressure of CCl4 is 1.24. Use the vapor pressure/tot pressure to get mole fraction in vapor:
Mole fraction C6H6= 1(0.5)/(1.24(.5)+1(.5))= 0.446
Where .5 is mole fraction in solution because they are equimolar
Then
Mole fraction CCl4= 1-.446= .554
Sorry, I didn't realize that data didn't attach...here it is..thank you for all your help!
Substance ∆Gf°
C6H6 (l) 124.50 kJ/mol
C6H6 (g) 129.66 kJ/mol
CCl4 (l) -65.21 kJ/mol
CCl4 (g) -60.59 kJ/mol
To determine the composition in mole fraction of the condensed vapor, we need to use Raoult's law. Raoult's law states that the partial pressure of each component in an ideal solution is directly proportional to its mole fraction in the solution.
In this case, we have an equimolar solution of carbon tetrachloride (CCl4) and benzene (C6H6). Since they form an ideal solution, we can assume that Raoult's law holds true.
Let's denote the mole fraction of carbon tetrachloride as x1 and the mole fraction of benzene as x2.
According to Raoult's law, the partial pressure of each component is given by:
P1 = x1 * P°1
P2 = x2 * P°2
where P1 and P2 are the partial pressures of CCl4 and C6H6, respectively. P°1 and P°2 are the vapor pressures of pure CCl4 and C6H6 at 25°C.
We need the vapor pressure data of CCl4 and C6H6 at 25°C to proceed further. Please provide the vapor pressure values for both components.