A solution contains 3.75g of nonvolatile pure hydrocarbon in 95g acetone. The boiling points of pure acetone and the solution are 55.95C and 56.50C, respectively. The molal boiling point constant of acetone is 1.71 C*kg/mol. What is the molar mass of the hydrocarbon?
120g/mol
i have no response
will be slightly lower than 56.50 degree Celsius
Well, let's start by finding the change in boiling point using the equation:
ΔTb = Kb * m
Where ΔTb is the change in boiling point, Kb is the molal boiling point constant, and m is the molality of the solution.
Given that the change in boiling point is 0.55°C and the molal boiling point constant is 1.71°C*kg/mol, we can solve for the molality:
0.55°C = 1.71°C*kg/mol * m
Solving for m, we find that the molality is approximately 0.322 mol/kg.
To find the molar mass of the hydrocarbon, we need to know the number of moles of the hydrocarbon in the solution. We can find this by using the molality and the mass of acetone:
moles of hydrocarbon = molality * mass of acetone
mass of acetone = mass of solution - mass of hydrocarbon
Given that the mass of the hydrocarbon is 3.75g and the mass of the solution is 95g, we can substitute these values into the equation to find the moles of the hydrocarbon:
moles of hydrocarbon = 0.322 mol/kg * (95g - 3.75g)
moles of hydrocarbon = 30.692 mol
Finally, to find the molar mass of the hydrocarbon, we divide the mass of the hydrocarbon by the number of moles:
molar mass = mass of hydrocarbon / moles of hydrocarbon
molar mass = 3.75g / 30.692 mol
molar mass ≈ 0.122 g/mol
So, the molar mass of the hydrocarbon is approximately 0.122 g/mol.
To find the molar mass of the hydrocarbon, we can use the formula:
ΔTb = Kb * m
Where:
ΔTb = change in boiling point
Kb = molal boiling point constant
m = molality of the solution
First, let's calculate the change in boiling point (ΔTb):
ΔTb = Tb(solution) - Tb(solvent)
ΔTb = 56.50°C - 55.95°C
ΔTb = 0.55°C
Now, we can calculate the molality (m) of the solution:
m = moles of solute / mass of solvent (in kg)
The mass of the solvent (acetone) is 95g, which is equal to 0.095kg.
To find the moles of solute (hydrocarbon), we need to convert the mass of hydrocarbon to moles. We can do this by dividing the mass of hydrocarbon by its molar mass.
Now, let x be the molar mass of the hydrocarbon (in g/mol).
moles of hydrocarbon = mass of hydrocarbon / molar mass of hydrocarbon
moles of hydrocarbon = 3.75g / x
Substituting these values into the molality formula:
m = (3.75g / x) / 0.095kg
m = 3.75g / (x * 0.095kg)
Now, we can substitute the obtained ΔTb and molality (m) values into the formula to find Kb, the molal boiling point constant:
0.55°C = Kb * (3.75g / (x * 0.095kg))
Next, rearrange the equation to solve for Kb:
Kb = 0.55°C * (x * 0.095kg) / 3.75g
Kb = 0.01395°C * kg / g * x
Now that we have the value of Kb, which is the molal boiling point constant, we can substitute it back into the formula and solve for the molar mass of the hydrocarbon:
1.71°C * kg / mol = 0.01395°C * kg / g * x
Finally, solve for x:
x = (1.71°C * kg / mol) / (0.01395°C * kg / g)
x ≈ 122.58 g/mol
Therefore, the molar mass of the hydrocarbon is approximately 122.58 g/mol.
delta t = Kb*molality
Solve for molality
molality = moles/kg solvent
Solve for moles
moles = grams/molar mass
Solve for molar mass.