Reviewing for final (this should be basic but...I am stuck):
Describe how you would prepare 500.0 grams of a solution of sucrose, C12H22O11, in water which the mole fraction of sucrose is 0.125.
I feel like somehow this is a molality question too :(
Thank you for any input.
Xsucrose = 0.125
XH2O = 0.875
0.125 x molar mass sucrose = about 43g (but you can do it better than that, and should).
0.875 x molar mass H2O = about 15.75g
Just to check, 43/342 = 0.125
15.75/18 = 0.875 and
0.125/(0.125+0.875) = 0.125 etc.
Now how much will all of that weigh?
43 g + 15.75g = about 58.5 g which is far short of the 500 g you want. So scale it up. The easy way to do that is to see what percent 43 is of 58.5 and what percent 15.75 is of 58.5. Find grams then of each at that percentage of 500 g and check to see that you still have the mole fractions right. I checked it out and it works fine.
Oh thank you!
43 is 73.11% of 58.52 and
15.76 is 26.93% of 58.52
so when we scale it up to 500g we got 365g of sucrose and 135g of water!
When I worked it I came out with 368.5 g sucrose and 134.61 g H2O and I expect that is close enough since we probably didn't round the same and we may have used slightly different values for molar mass. I used 342 for sucrose and 18 for water. I used 58.5 for the initial mass.
To prepare a solution with a mole fraction of sucrose, you need to follow a step-by-step process. Let's break it down:
Step 1: Calculate the number of moles of sucrose required.
To do this, you need to know the molar mass of sucrose, which is 342.3 g/mol (rounded to one decimal place).
Given that the mole fraction (Xsucrose) = 0.125, the mole fraction of water (Xwater) would be 1 - Xsucrose, which is 0.875.
Step 2: Calculate the number of moles of water required.
To calculate this, you can assume a total mass of 500.0 grams for the solution. Since the mole fraction of water is 0.875, you can use the formula:
moles of water (H2O) = (mass of water / molar mass of water) = (500.0 g × 0.875) / 18.0 g/mol
Step 3: Convert the number of moles of sucrose to grams.
Given the mole fraction of sucrose (Xsucrose) is 0.125, you can find the moles of sucrose using the formula:
moles of sucrose (C12H22O11) = Xsucrose × (mass of water / molar mass of sucrose) = 0.125 × (500.0 g × 0.125) / 342.3 g/mol
Step 4: Calculate the mass of sucrose required.
To find the mass, multiply the moles of sucrose by the molar mass of sucrose:
mass of sucrose (C12H22O11) = moles of sucrose × molar mass of sucrose = moles × 342.3 g/mol
After completing these calculations, you will have the mass of sucrose required to prepare a 500.0 g solution with a mole fraction of 0.125 for sucrose.
Regarding your concern about molality, it is not directly related to this question. Molality (m) is a different concept that refers to the number of moles of solute per kilogram of solvent. In this case, the mole fraction is being used to determine the composition of the solution rather than molality.
Ah, preparing solutions, the great chemistry challenge! Don't worry, I'm here to help you out and add a little humor along the way. Let's tackle this.
To prepare a solution of sucrose in water, we need to first calculate the amount of sucrose needed. Since we are given the mole fraction of sucrose, we can use it to find the moles of sucrose we need.
Step 1: Moles of Sucrose
Given that the mole fraction of sucrose is 0.125, we can assume that 0.125 moles of the final solution consist of sucrose.
Step 2: Moles of Water
To find the moles of water, we subtract the moles of sucrose from one. So, 1 - 0.125 = 0.875 moles of water.
Step 3: Mass of Water
To find the mass of water, we multiply the moles of water by its molar mass, which is approximately 18 g/mol. So, 0.875 moles * 18 g/mol = 15.75 grams of water.
Step 4: Total Mass of Solution
Now, to find the total mass of the solution, we add the mass of sucrose and the mass of water. 500 g (total mass) - 15.75 g (mass of water) = 484.25 g (mass of sucrose).
So, to prepare 500.0 grams of a sucrose solution with a mole fraction of 0.125, you would need to dissolve approximately 484.25 grams of sucrose in approximately 15.75 grams of water. Voila!
Remember, always approach chemistry problems with a smile and a dash of humor. Good luck with your final review!