Okay so I know how I would normally determine molar mass of a compound *get out periodic table, sum up elements present, eg. H20 = [2(1.008)+16.00]g/mol*
But this is for a lab class and they want us to derive it.
Info found: Ethylene glycol (C2H6O2 according to book) dissolved in water:
mass water: 150 g
mass ethylene glycol: 50 g
found boiling point: 103 C
MW ethylene glycol: ?
We've been using the boiling point elevation equation a lot
^T(boil)=i*k(boil)*molality(m)
I suppose the molality would be:
1.) 50g solute*(1 mole solute/62.068g solute)=0.81 mol solute
2.) 150g solvent*(1 kg solvent/1000 g solvent)=0.150kg solvent
3.) m = 0.81 mol solute/0.150kg solvent
m = 5.4
van't Hoff factor of ethylene glycol is (I believe) 1 (organic compound)
this would make k(boil)=^T(boil)/m or more specifically ~0.74 (technically 20/27 but that would violate sig. figs)
but I'm not sure what any of this has to do w/ calculating the molecular weight.
Thank you in advance.
delta T = Kb*m
3= 0.512*m
Solve for m
molality = moles/kg solvent
molality from above x 0.150 = moles ethylene glycol. Solve for moles.
moles = grams/molar mass
You have moles and grams, solve for molar mass. Assuming 103 is your best T measurment, I come up with about 57. The molar mass from the periodic table is about 62. Error about 8%.
To calculate the molecular weight (MW) of ethylene glycol (C2H6O2), one way is to use the boiling point elevation equation, as you mentioned. To do this, you need to know the boiling point elevation constant (k(boil)) for the solvent and the change in boiling point (^T(boil)).
In this case, the change in boiling point is given as 103°C. To convert this to Kelvin, you need to add 273.15:
^T(boil) = 103 + 273.15 = 376.15 K
Next, we can calculate the molality (m) using the given mass of the solute (ethylene glycol) and the mass of the solvent (water):
1. Calculate the number of moles of ethylene glycol:
Given: mass of ethylene glycol = 50 g, molar mass of ethylene glycol = ?
To find the molar mass of ethylene glycol, we need to determine the number of moles present in 50 g of the compound.
Using the periodic table, the molar masses of carbon (C), hydrogen (H), and oxygen (O) are approximately 12.01 g/mol, 1.008 g/mol, and 16.00 g/mol, respectively. Therefore:
Molar mass of C2H6O2 = (2 * 12.01) + (6 * 1.008) + (2 * 16) = 62.068 g/mol
Now, we can calculate the number of moles of ethylene glycol:
Moles of ethylene glycol = mass of ethylene glycol / molar mass of ethylene glycol
= 50 g / 62.068 g/mol
≈ 0.806 moles
2. Calculate the molality (m) of the ethylene glycol solution:
Given: mass of water = 150 g, molality (m) = ?
Molality (m) = moles of solute / mass of solvent (in kg)
= 0.806 moles / (150 g / 1000 g/kg)
= 5.38 mol/kg
3. The van't Hoff factor (i) for ethylene glycol is 1, as it is an organic compound.
Now that we have ^T(boil) = 376.15 K, m = 5.38 mol/kg, and i = 1, we can rearrange the boiling point elevation equation to solve for the boiling point elevation constant (k(boil)):
k(boil) = ^T(boil) / (i * m)
= 376.15 K / (1 * 5.38 mol/kg)
= 69.92 K·kg/mol
Finally, to calculate the molar mass of ethylene glycol (MW), we can rearrange the boiling point elevation equation again:
MW = ^T(boil) / (k(boil) * m)
= 376.15 K / (69.92 K·kg/mol * 5.38 mol/kg)
≈ 1.089 g/mol
Therefore, the molecular weight of ethylene glycol (C2H6O2) is approximately 1.089 g/mol.