A solution of hexane in the solvent (CH3)2CO has a mole fraction of CH3(CH2)4CH3 of 0.114. What mass (g) of the solution must be taken if 1690 g of hexane is needed?

Molar Mass (g/mol)
CH3(CH2)4CH3 100.21
(CH3)2CO 58.05

Density (kg/L):
CH3(CH2)4CH3 0.6838
(CH3)2CO 0.7899

Name/Formula:
hexane
CH3(CH2)4CH3
acetone
(CH3)2CO

0.114 = X(hexane)/X(hexane)+X(acetone)

X(hexane) = 1690 g hexane/100.21
X(acetone) = grams acetone/58.05
You have only one unknown. Solve for grams acetone. Then g acetone + 1690 = total grams.Check my thinking. Check my work. Post your work if you need further assistance.

To solve this problem, we need to use the concept of mole fraction and the given molar masses and densities of hexane and acetone.

First, let's calculate the moles of hexane needed using its given molar mass:
Moles of hexane = mass of hexane / molar mass of hexane
Moles of hexane = 1690 g / 100.21 g/mol
Moles of hexane = 16.879 mol

Next, let's convert the mole fraction of hexane in the solution to the moles of hexane:
Moles of hexane in the solution = mole fraction of hexane × Total moles of both components in the solution
Moles of hexane in the solution = 0.114 × (moles of hexane + moles of acetone)

Since the total moles of the components in the solution are moles of hexane + moles of acetone, we can substitute the value of moles of hexane from the previous step into the equation:
0.114 × (moles of hexane + moles of acetone) = 16.879 mol

Now, let's solve this equation to find the moles of acetone:
0.114 × moles of hexane + 0.114 × moles of acetone = 16.879 mol
0.114 × moles of acetone = 16.879 mol - 0.114 × moles of hexane
0.114 × moles of acetone = 16.879 mol - 0.114 × 16.879 mol
0.114 × moles of acetone = 14.976 mol
moles of acetone = 14.976 mol / 0.114

Now that we have the moles of acetone, let's convert it to mass using the given density:
Mass of acetone = moles of acetone × molar mass of acetone
Mass of acetone = moles of acetone × 58.05 g/mol

Finally, to find the total mass of the solution, we add the mass of hexane to the mass of acetone:
Total mass of the solution = mass of hexane + mass of acetone

Therefore, to find the mass of the solution required, you would need to perform these calculations using the given values.