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.
MOL FRACTION H2O + MOL FRACTION C12H22O11 = 1
THEN
MOL FRACTION H2O = 0.8
MOL FRACTION H2O = MOL H20 / TOTAL MOL
MOL H2O = 200/18 = 11.1
THEN
0.8=11.1/(11.1+MOL C12H22O11)
MOL C12H22O11 = 0.26MOL
MASS OF C12H22O11 = MOL * MOLAR MASS
MASS OF C12H22O11 =0.26*342
MASS OF C12H22O11 = 88.92 GRAM
To calculate the grams of sucrose needed, we need to use the mole fraction equation:
Mole fraction of sucrose (Xsucrose) = moles of sucrose / total moles
Given that the mole fraction of sucrose is 0.2 and the total moles is equal to the sum of moles of sucrose and moles of water, we can set up the equation:
0.2 = moles of sucrose / (moles of sucrose + moles of water)
Since the mole fraction of sucrose is the ratio of moles of sucrose to the total moles, we can rewrite the equation as:
0.2 = moles of sucrose / (moles of sucrose + (mass of water / molar mass of water))
Now let's solve for the moles of sucrose:
0.2 = moles of sucrose / (moles of sucrose + (200 g / 18.015 g/mol))
Rearranging the equation to solve for moles of sucrose:
0.2 * (moles of sucrose + (200 g / 18.015 g/mol)) = moles of sucrose
Now we can solve for moles of sucrose:
0.2 * (moles of sucrose + 11.097 mol) = moles of sucrose
0.2 moles of sucrose + 0.2 * 11.097 mol = moles of sucrose
0.2 * 11.097 mol = 0.8 * moles of sucrose
2.2194 mol = 0.8 * moles of sucrose
moles of sucrose = 2.2194 mol / 0.8
moles of sucrose = 2.77425 mol
Finally, let's calculate the grams of sucrose using the moles of sucrose and molar mass of sucrose:
grams of sucrose = moles of sucrose * molar mass of sucrose
grams of sucrose = 2.77425 mol * (12.011 g/mol + 1.00794 g/mol + 15.9994 g/mol)
grams of sucrose = 70.03 g
Therefore, you would need approximately 70.03 grams of sucrose to dissolve in 200 g of water to make a solution with a mole fraction of sucrose of 0.2.
To find the number of grams of sucrose needed to make a solution with a desired mole fraction, we need to follow these steps:
Step 1: Convert the given mole fraction of sucrose into moles.
Step 2: Calculate the total moles of the solution.
Step 3: Convert the moles of sucrose into grams using the molar mass of sucrose.
Step 1: Convert the mole fraction into moles.
The mole fraction of sucrose (Xsucrose) is defined as:
Xsucrose = moles of sucrose / total moles of solution
Given that Xsucrose = 0.2, we can rearrange the equation to solve for moles of sucrose:
moles of sucrose = Xsucrose * total moles of solution
Step 2: Calculate the total moles of the solution.
To find the total moles of the solution, we need the masses and molar masses of both sucrose and water.
Mass of water = 200 g
Molar mass of water (H2O) = 18.015 g/mol
Using the formula:
moles = mass / molar mass
We can calculate the moles of water:
moles of water = 200 g / 18.015 g/mol
Step 3: Convert the moles of sucrose into grams.
To do this, we need the molar mass of sucrose (C12H22O11).
Molar mass of sucrose = (12 * 12.011 g/mol) + (22 * 1.008 g/mol) + (11 * 15.999 g/mol)
= 342.296 g/mol
Now, we can calculate the grams of sucrose:
grams of sucrose = moles of sucrose * molar mass of sucrose
Substituting the values we have calculated, we get:
grams of sucrose = (Xsucrose * total moles of solution) * molar mass of sucrose
grams of sucrose = (0.2 * (200 g / 18.015 g/mol)) * 342.296 g/mol
Calculating this expression will give you the number of grams of sucrose required to make the solution.