A solution is made by dissolving 27.8 g of nicotine (Molar Mass = 160 g/mol) in 145 g of cyclohexane (C6H12) to form 142 mL of solution. Calculate the mole fraction of the solute and the molarity, respectively, of this solution.
mols nicotine = grams/molar mass = ?
mols C6H12 = grams/molar mass
Find total mols.
XC6H12 = nC6H12/total mols.
M C6H12 = mols C6H12/L solution = ?
To find the mole fraction of the solute, we need to calculate the moles of both the solute (nicotine) and the total moles of the solution.
Step 1: Calculate the moles of nicotine.
Moles of nicotine = Mass of nicotine / Molar mass of nicotine
= 27.8 g / 160 g/mol
= 0.17375 mol
Step 2: Calculate the moles of cyclohexane.
Moles of cyclohexane = Mass of cyclohexane / Molar mass of cyclohexane
= 145 g / 84 g/mol
= 1.7262 mol
Step 3: Calculate the total moles of the solution.
Total moles = Moles of nicotine + Moles of cyclohexane
= 0.17375 mol + 1.7262 mol
= 1.89995 mol
Step 4: Calculate the mole fraction of the solute.
Mole fraction of solute = Moles of nicotine / Total moles
= 0.17375 mol / 1.89995 mol
≈ 0.0914
To calculate the molarity of the solution, we need to convert the volume of the solution from milliliters (mL) to liters (L).
Step 5: Convert the volume of the solution from mL to L.
Volume of solution = 142 mL × 1 L/1000 mL
= 0.142 L
Step 6: Calculate the molarity of the solution.
Molarity (M) = Moles of solute / Volume of solution (in L)
= 0.17375 mol / 0.142 L
≈ 1.222 M
Therefore, the mole fraction of the solute is approximately 0.0914 and the molarity of the solution is approximately 1.222 M.
To calculate the mole fraction of the solute and the molarity of the solution, we need to use the formulas:
1. Mole fraction (X) = number of moles of solute / total number of moles in the solution
2. Molarity (M) = number of moles of solute / volume of solution in liters
Let's start by calculating the number of moles of nicotine (solute):
Step 1: Calculate the number of moles of nicotine (solute)
Number of moles (n) = mass (m) / molar mass (M)
n = 27.8 g / 160 g/mol
n ≈ 0.17375 mol
Next, let's calculate the number of moles of cyclohexane (solvent):
Step 2: Calculate the number of moles of cyclohexane (solvent)
Number of moles (n) = mass (m) / molar mass (M)
n = 145 g / 84.18 g/mol
n ≈ 1.72364 mol
Now, let's calculate the mole fraction of the solute:
Step 3: Calculate the mole fraction of the solute (nicotine)
Mole fraction (X) = number of moles of solute / total number of moles in the solution
X = 0.17375 mol / (0.17375 mol + 1.72364 mol)
X ≈ 0.0919
The mole fraction (X) of the solute (nicotine) is approximately 0.0919.
Finally, let's calculate the molarity of the solution:
Step 4: Calculate the molarity of the solution
Molarity (M) = number of moles of solute / volume of solution in liters
Volume of solution = 142 mL = 142/1000 L
M = 0.17375 mol / 0.142 L
M ≈ 1.2236 M
The molarity (M) of the solution is approximately 1.2236 M.