A solution is prepared by mixing 0.0400 mol CH2Cl2 and 0.0800 mol CH2Br2 at 25 degrees C. Assume solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at 25 C. At 25 C, vaporpressure of pure CH2Cl2 and pure CH2Br2 are 133 and 11.4 torr.
Thanks. My answer is still coming up wrong, thought it was sig figs, but I'm getting 43.9 and 7.52.......mole fractions are .33 and .66. What gives???
Sum the moles to get total moles.
mole fraction CH2Cl2 = #moles/total moles.
mole fraction CH2Br2 = #moles/total moles.
vapor pressure CH2Cl2 = mole fraction CH2Cl2 x normal vapor pressure CH2Cl2.
vapor pressure CH2Br2 = mole fraction Ch2Br2 x normal vapor pressure CH2Br2.
Total pressure is the sum of the partial pressures of each component.
I didn't round like you did AND you short changed the s.f. You are allowed three from 0.0800 and 0.400 but you rounded to 2. I leave those extra 3s and 6s in the calculator and make the other calculations.
So I divide 0.04/0.12 = 0.3333333 and multiply on the spot by 133 to obtain 44.33 torr.
0.08/0.12 = 0.666666 and multiply on the spot by 11.4 = 7.60 (note that by rounding to 0.66 the number is 7.52 and rounding to 0.67 the number is 7.63---a big difference with just one digit). So I would add 44.33 and 7.60 = 51.93. You are allowed three s.f. and I would round that final number to 51.9 torr. Check my work.
To calculate the composition of the vapor in terms of mole fractions, we need to determine the mole fractions of each component in the liquid mixture and use the mole fraction ratio to calculate the composition of the vapor.
Step 1: Calculate the total moles of the mixture
To find the total moles of the mixture, add the moles of CH2Cl2 and CH2Br2 together:
Total moles = moles of CH2Cl2 + moles of CH2Br2
Total moles = 0.0400 mol + 0.0800 mol
Total moles = 0.1200 mol
Step 2: Calculate the mole fraction of CH2Cl2
The mole fraction (X) of a component is calculated by dividing the moles of that component by the total moles of the mixture:
Mole fraction of CH2Cl2 = moles of CH2Cl2 / total moles
Mole fraction of CH2Cl2 = 0.0400 mol / 0.1200 mol
Mole fraction of CH2Cl2 = 1/3 or 0.333 (rounded to three decimal places)
Step 3: Calculate the mole fraction of CH2Br2
Similarly, calculate the mole fraction of CH2Br2:
Mole fraction of CH2Br2 = moles of CH2Br2 / total moles
Mole fraction of CH2Br2 = 0.0800 mol / 0.1200 mol
Mole fraction of CH2Br2 = 2/3 or 0.667 (rounded to three decimal places)
Step 4: Calculate the composition of the vapor
The composition of the vapor will be the same as the composition of the liquid mixture since an ideal solution assumes that there is no preferential evaporation of either component. Therefore, the composition of the vapor will be:
Mole fraction of CH2Cl2 in vapor = Mole fraction of CH2Cl2 in liquid = 0.333
Mole fraction of CH2Br2 in vapor = Mole fraction of CH2Br2 in liquid = 0.667
So, the composition of the vapor in terms of mole fractions at 25°C is approximately 0.333 for CH2Cl2 and 0.667 for CH2Br2.