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 0.2? Answer in units of g.

let moles C12H22O11 = x

moles H2O = 60/18 = 3.33 but check that.
Xsucrose = x/total moles and
0.2 = x/(x+3.33)
solve for x = moles sucrose.
g = mols x molar mass.
Check my work.

To find out how many grams of sucrose (C12H22O11) must be dissolved in 60 g of water to make a solution with a mole fraction of 0.2, we need to follow these steps:

Step 1: Calculate the number of moles of water.
Given that the mass of water is 60 g and we know that the molar mass of water (H2O) is approximately 18 g/mol, we can calculate the number of moles using the formula:

Number of moles = Mass / Molar mass
Number of moles of water = 60 g / 18 g/mol = 3.33 mol

Step 2: Calculate the number of moles of sucrose.
The mole fraction of sucrose is given as 0.2, which means that the mole fraction of water is 1 - 0.2 = 0.8. Since the mole fraction is a ratio, we can set up the following equation:

Mole fraction of sucrose = Moles of sucrose / (Moles of sucrose + Moles of water)

0.2 = Moles of sucrose / (Moles of sucrose + 3.33 mol)

Simplifying the equation:

0.2 * (Moles of sucrose + 3.33 mol) = Moles of sucrose

0.2 * Moles of sucrose + 0.2 * 3.33 mol = Moles of sucrose

0.2 * Moles of sucrose - Moles of sucrose = -0.2 * 3.33 mol

-0.8 * Moles of sucrose = -0.666 mol

Moles of sucrose = -0.666 mol / -0.8

Moles of sucrose = 0.833 mol

Step 3: Calculate the mass of sucrose.
Now that we know the number of moles of sucrose, we can calculate the mass of sucrose using its molar mass. The molar mass of sucrose (C12H22O11) is approximately 342 g/mol.

Mass of sucrose = Moles of sucrose * Molar mass

Mass of sucrose = 0.833 mol * 342 g/mol

Mass of sucrose = 284.89 g

Therefore, approximately 284.89 grams of sucrose must be dissolved in 60 g of water to make a solution with a mole fraction of sucrose of 0.2.