Calculate the molality (m) of a 1820 g sample of a solution of the solute hexane dissolved in the solvent C6H6 if the sample contains 0.419 kg of hexane.
Remember the definition of molality.
m = # moles solute/kg solvent.
Total g solution = 1820
mass hexane (C6H14) = 419
mass solvent (C6H6) = 1820-419 = 1401 g.
moles C6H14 = 419/molar mass.
kg solvent = 1.401
You do the math. Check my numbers.
To calculate the molality (m) of a solution, we need to use the formula:
m = moles of solute / mass of solvent in kilograms
Step 1: Convert the mass of solute to moles.
To do this, we need to know the molar mass of hexane (C6H14). The molar mass of carbon (C) is 12.01 g/mol, and hydrogen (H) is 1.01 g/mol.
Let's calculate the molar mass of hexane:
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
6 carbon atoms * 12.01 g/mol = 72.06 g/mol
14 hydrogen atoms * 1.01 g/mol = 14.14 g/mol
Total molar mass of hexane (C6H14) = 72.06 g/mol + 14.14 g/mol = 86.20 g/mol
Now, we can calculate the moles of hexane in the sample:
moles of hexane = mass of hexane / molar mass of hexane
moles of hexane = 0.419 kg * 1000 g/kg / 86.20 g/mol
Step 2: Convert the mass of solvent to kilograms.
The mass of the solvent is 1820 g. Since we want the mass of the solvent in kilograms, we divide it by 1000.
mass of solvent = 1820 g / 1000 = 1.820 kg
Step 3: Substitute the values into the molality formula.
m = moles of solute / mass of solvent in kilograms
m = (0.419 kg * 1000 g/kg / 86.20 g/mol) / 1.820 kg
Simplifying the expression, we get:
m = 4.865 mol / 1.820 kg
Finally, calculating the molality (m):
m ≈ 2.676 mol/kg
Therefore, the molality of the solution is approximately 2.676 mol/kg.