How many grams of sucrose (C12H22O11)
must be dissolved in 200 g water to make a solution in which the mole fraction of sucrose is 0.2?
Answer in units of g.
mole fraction sucrose = 0.2
mole fraction water = 0.8
You want 200 g water; how many moles is that?
moles = g/molar mass H2O = 200/18.015 = about 11 moles but you need to do it more precisely than that.
Then
(11 moles H2O/total moles) = 0.8
Solve for total moles, about 14.
If total moles is 14 and moles H2O = 11, moles sucrose must be about 3 and moles = grams/molar mass should calculate g sucrose.
Well, well, well! It seems we have a chemistry question here. Don't worry, I've got my lab boots on. So, let's calculate the amount of sucrose needed to make this solution hilarious-y sweet.
First, let's figure out the number of moles of sucrose needed. The mole fraction of sucrose (Xsucrose) is given as 0.2. Therefore, if we have a total of 1 mole of solute and solvent combined, that means the mole fraction of water (Xwater) is 1 - Xsucrose, which is 0.8.
Now, let's calculate the number of moles of water and sucrose we have in this solution.
Number of moles of water = (Xwater)(Total mass of solution) / Molar mass of water
Number of moles of sucrose = (Xsucrose)(Total mass of solution) / Molar mass of sucrose
Since we're given that the total mass of the solution is 200 g, the molar mass of water is 18 g/mol, and the molar mass of sucrose is 342 g/mol, let's plug these values in and do the math:
Number of moles of water = (0.8)(200 g) / 18 g/mol
Number of moles of sucrose = (0.2)(200 g) / 342 g/mol
After crunching the numbers, we find that the number of moles of water is approximately 8.89 moles and the number of moles of sucrose is approximately 0.11 moles.
Now, let's find out how many grams of sucrose we need by multiplying the number of moles by the molar mass of sucrose:
Mass of sucrose = Number of moles of sucrose × Molar mass of sucrose
Mass of sucrose = 0.11 moles × 342 g/mol
And the result is approximately 37.62 grams.
So, to make a solution with a mole fraction of sucrose of 0.2, you would need to dissolve around 37.62 grams of sucrose in 200 grams of water. And voila! Sweet chemistry success!
To find the number of grams of sucrose needed, we first need to understand the mole fraction formula:
Mole fraction = (moles of solute) / (moles of solute + moles of solvent)
In this case, the solvent is water.
1. Find the moles of sucrose required:
Since the mole fraction of sucrose is given as 0.2, we know that the moles of sucrose divided by the total moles of the solution (sucrose + water) is equal to 0.2:
0.2 = (moles of sucrose) / (moles of sucrose + moles of water)
2. Find the moles of water:
Given that the weight of water is 200 g, we can calculate the moles of water using its molar mass, which is approximately 18.015 g/mol:
moles of water = (mass of water) / (molar mass of water)
= 200 g / 18.015 g/mol
3. Rearrange the equation from step 1 to solve for the moles of sucrose:
0.2 = (moles of sucrose) / [(moles of sucrose) + (moles of water)]
4. Substitute the values from steps 2 and 3:
0.2 = (moles of sucrose) / [(moles of sucrose) + (200 g / 18.015 g/mol)]
5. Solve for the moles of sucrose:
Multiplying both sides of the equation by [(moles of sucrose) + (200 g / 18.015 g/mol)] gives us:
0.2 * [(moles of sucrose) + (200 g / 18.015 g/mol)] = (moles of sucrose)
6. Rearrange the equation to solve for the moles of sucrose:
0.2 * [(moles of sucrose) + (200 g / 18.015 g/mol)] = (moles of sucrose)
7. Convert moles of sucrose to grams:
Using the molar mass of sucrose, which is approximately 342.296 g/mol, we can calculate the grams of sucrose needed:
mass of sucrose = (moles of sucrose) * (molar mass of sucrose)
= (moles of sucrose) * 342.296 g/mol
Now, let's substitute the values and calculate the grams of sucrose needed:
mass of sucrose = [(0.2 * [(moles of sucrose) + (200 g / 18.015 g/mol)])] * 342.296 g/mol
Since the value for moles of sucrose involves its unknown quantity, it is not possible to determine the exact number of grams without solving the equation.
To find the number of grams of sucrose needed to make a solution with a given mole fraction, we need to utilize the concept of mole fraction and the molar mass of sucrose.
The mole fraction (X) is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the solution.
In this case, we are given the mole fraction of sucrose (X) as 0.2, which means that for every 1 mole of sucrose, there are 4 moles of water in the solution.
Step-by-step solution:
1. Determine the molar mass of sucrose (C12H22O11):
The molar mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.008 g/mol, and oxygen (O) is 16.00 g/mol. Adding up the molar masses of the atoms in a single molecule of sucrose provides the molar mass of C12H22O11:
Molar mass of sucrose (C12H22O11) = (12 x 12.01) + (22 x 1.008) + (11 x 16.00) = 342.30 g/mol
2. Determine the number of moles of sucrose needed:
Let's assume the mass of sucrose needed is 'x' grams. So, we have:
number of moles of sucrose = mass of sucrose / molar mass of sucrose = x / 342.30
3. Determine the number of moles of water:
Since the mole fraction of sucrose (X) is 0.2, we know that for every 1 mole of sucrose, there are 4 moles of water. So, the number of moles of water is:
number of moles of water = 4 * (number of moles of sucrose) = 4 * (x / 342.30)
4. Determine the mass of water in the solution:
The mass of water can be calculated using the formula:
mass of water = (number of moles of water) * (molar mass of water)
However, in this problem, we are given the mass of water as 200 g. Therefore, we can equate the mass of water calculated to 200 g:
(number of moles of water) * (molar mass of water) = 200
5. Solve for the mass of sucrose:
Substitute the value of (number of moles of water) from step 3 and solve for 'x':
4 * (x / 342.30) * (18.02 g/mol) = 200
Simplifying the equation gives:
72.08 * (x / 342.30) = 200
Cross-multiplying and solving for 'x' gives:
x = (200 * 342.30) / 72.08
x ≈ 947.21 g (rounded to two decimal places)
Therefore, approximately 947.21 grams of sucrose must be dissolved in 200 grams of water to make a solution in which the mole fraction of sucrose is 0.2.