How many grams of sucrose (C12H22O11)
must be dissolved in 60 g water to make a
solution in which the mole fraction of sucrose is 0.4?
Answer in units of g.
60 g H2O = ? mols. mol = grams/molar mass.
mols sucrose = grams/molar mass.
Xsucrose = mols sucrose/total mols.
You know Xsucrose. Substitute that into X formula and solve for g sucrose. Post your work if you get stuck.
I don't really understand how to set it up. I'm to figure out my moles for water but after that I'm stuck.
mols H2O = 60g/18 = 3.33
mols sucrose = n
total mol = 3.33 + n
Xsucrose = mols sucrose/(total mols)
0.4 = [n/(n+3.33)]
Solve for n = mols sucrose.
Then mols sucrose = grams sucrose/molar mass sucrose.
You know mols sucrose from the above calculation. You know molar mass sucrose (about 342), solve for grams and you have it.
To find the number of grams of sucrose (C12H22O11) that must be dissolved in 60 g of water to make a solution with a mole fraction of 0.4, we can use the following steps:
1. Determine the mole fraction of sucrose in the solution:
Mole fraction of sucrose (xS) = moles of sucrose (nS) / total moles of solute and solvent
Given: xS = 0.4
2. Calculate the moles of water (nW) in the solution:
Given: Mass of water (mW) = 60 g
Molar mass of water (MW) = 18.015 g/mol
nW = mW / MW
3. Determine the moles of sucrose (nS) in the solution:
Use the equation:
xS = nS / (nS + nW)
Rearrange the equation to solve for nS:
nS = xS * (nS + nW)
4. Substitute the given values and solve for nS:
0.4 = nS / (nS + nW)
Multiply through by (nS + nW):
0.4 * (nS + nW) = nS
Distribute the 0.4:
0.4 * nS + 0.4 * nW = nS
Rearrange the equation to solve for nS:
nS - 0.4 * nS = 0.4 * nW
Simplify:
0.6 * nS = 0.4 * nW
Divide through by 0.6:
nS = (0.4 * nW) / 0.6
Substitute the value of nW and solve:
nS = (0.4 * (60 g / 18.015 g/mol)) / 0.6
5. Calculate the mass of sucrose (mS) in grams:
Given: Molar mass of sucrose (MS) = 342.3 g/mol
mS = nS * MS
Now we have the formula and the steps, let's calculate the mass of sucrose (mS):
mS = [(0.4 * (60 g / 18.015 g/mol)) / 0.6] * 342.3 g/mol
Calculating this expression will give you the answer, in units of grams, for the mass of sucrose that must be dissolved in 60 g of water to obtain a solution with a mole fraction of sucrose equal to 0.4.