How would i found out the freezing point of a solution which has 0.05mol of acetic acid dissolved into 125g of benzene? Benzene melts at 5.5C and has a constant of 5.1C/m. The acid forms a dimer (what is this and how does it affect the calculations?)
A dimer is a molecule from from two of the same atoms or molecules. Acetic acid dimer would be (HC2H3O2)2
When a dimer forms, there would be half as many molecules of solute in solution when you apply Raoult's law for the freezing point lowering. They apparently tell you the Raoult's Law coefficient for benzene. You need to calculate the molal concentration of the acetic acid dimer, and apply the law.
To find out the freezing point of the solution, you can use the principle of freezing point depression. This principle states that the presence of a non-volatile solute in a solvent will lower the freezing point of the solvent.
First, let's calculate the molal concentration of the acetic acid dimer in the solution. Molality (m) is defined as the moles of solute per kilogram of solvent.
Given:
Number of moles of acetic acid (solute) = 0.05 mol
Mass of benzene (solvent) = 125 g
To find the molality, we need to convert the mass of benzene to kilograms:
Mass of benzene = 125 g = 0.125 kg
Molality (m) = (moles of solute) / (mass of solvent in kg)
= (0.05 mol) / (0.125 kg)
= 0.4 mol/kg
Next, we need to apply Raoult's Law to calculate the freezing point depression. Raoult's Law states that the change in the freezing point (ΔTf) is proportional to the molal concentration of the solute (m). The constant of proportionality is called the cryoscopic constant or the freezing point depression constant.
Given:
Freezing point of benzene (pure solvent) = 5.5°C
Cryoscopic constant of benzene (Kf) = 5.1°C/m
We can use the formula:
ΔTf = Kf * m
Plugging in the values:
ΔTf = 5.1°C/m * 0.4 mol/kg
= 2.04°C
Finally, we need to find the freezing point of the solution.
Freezing point of solution = Freezing point of solvent - ΔTf
Freezing point of solution = 5.5°C - 2.04°C
= 3.46°C
Hence, the freezing point of the solution with 0.05 mol of acetic acid dissolved into 125 g of benzene is approximately 3.46°C.
The formation of dimers in acetic acid affects the calculations because it changes the effective concentration of the solute in solution. Since dimerization reduces the number of "effective" molecules of acetic acid in solution, the molal concentration of the dimer will be half of the calculated concentration using the number of moles given. Therefore, when applying Raoult's Law, we need to consider the molal concentration of the dimer rather than the individual molecules of acetic acid.