How many grams of sucrose (C12H22O11)
must be dissolved in 200 g water to make
a solution in which the mole fraction of su-
crose is 0.1?
Answer in units of g
200 g H2O is how many mols? That's g/molar mass.
total mol = n sucrose + n H2O
n sucrose = grams/molar mass sucrose
[n sucrose/(n sucroswe + nH2O)] = 0.1
Substitute grams/molar mass for n sucrose and solve for grams.
i got 11.098 for the moles for the first part. so do i add .1 to that?
No. Also if I divide 200/18.015 = 11.102 which is more s.f. than allowed but I carry them and drop at the end of the problem. You can't add them. 11.1 is mols H2O. The 0.1 is not mols sucrose; that 0.1 is the mole fraction of sucrose.
You must solve this.
[(x/342)/(x/342)+(11.1)] = 0.1 and solve for x = grams sucrose (Note: x/342 = mols sucrose)
To find the number of grams of sucrose that must be dissolved in water, we need to use the equation for mole fraction. The mole fraction (X) of a component in a solution is calculated by dividing the number of moles of that component by the total number of moles in the solution.
To solve this problem, we need the molecular weight of sucrose (C12H22O11). By adding up the atomic masses of each element in the compound, we find that the molecular weight of sucrose is approximately 342.3 g/mol.
First, we need to calculate the number of moles of sucrose required to make a solution with a mole fraction of 0.1. We are given that the total mass of the solution is 200 g and that the mole fraction of sucrose (X) is 0.1.
The number of moles of sucrose (n) can be calculated using the equation:
n = X * (total moles of the solution)
To find the total moles of the solution, we need to divide the mass of water by its molar mass. The molar mass of water (H2O) is approximately 18.015 g/mol.
Total moles of the solution (n_total) = Mass of water (m_water) / Molar mass of water (M_water)
n_total = 200 g / 18.015 g/mol ≈ 11.093 mol
Using the mole fraction equation, we can calculate the moles of sucrose (n_sucrose) required for a mole fraction of 0.1:
n_sucrose = X * n_total
n_sucrose = 0.1 * 11.093 mol ≈ 1.109 mol
Finally, we can calculate the mass of sucrose (m_sucrose) required by multiplying the number of moles by the molar mass of sucrose:
m_sucrose = n_sucrose * Molar mass of sucrose
m_sucrose = 1.109 mol * 342.3 g/mol ≈ 379.3 g
Therefore, approximately 379.3 grams of sucrose must be dissolved in 200 grams of water to make a solution with a mole fraction of sucrose equal to 0.1.