The freezing point depression constant for water is 1.86 degree C. If 5.00g Na2so4 is dissolved in 45.0g H20 ,the freezing point is changed by -3.82 degree C . Calculate the van't Hoff factor for Na2So4
To calculate the van't Hoff factor (i), we first need to determine the number of particles that Na2SO4 dissociates into when it dissolves in water.
Na2SO4 dissociates into three particles: 2 Na+ ions and 1 SO4^2- ion. Therefore, the van't Hoff factor (i) for Na2SO4 is 3.
The next step is to use the colligative property equation for freezing point depression to calculate the value of i. The equation is as follows:
ΔTf = i * Kf * m
Where:
- ΔTf is the change in freezing point (given as -3.82 degrees Celsius),
- i is the van't Hoff factor (which we need to find),
- Kf is the freezing point depression constant (given as 1.86 degrees Celsius/m),
- m is the molality of the solution (which we can calculate).
Molality (m) is defined as the moles of solute (Na2SO4) divided by the mass of the solvent (H2O) in kilograms.
First, we need to calculate the moles of Na2SO4 using its molar mass, which is calculated by adding up the atomic masses of the atoms in the compound:
Na: 2 * 22.99 g/mol = 45.98 g/mol
S: 32.07 g/mol
O: 4 * 16.00 g/mol = 64.00 g/mol
Total molar mass of Na2SO4 = 22.99 + 22.99 + 32.07 + 64.00 = 142.05 g/mol
Now, divide the given mass of Na2SO4 (5.00g) by its molar mass to obtain the number of moles:
moles of Na2SO4 = 5.00g / 142.05 g/mol
Next, we need to calculate the molality of the solution by dividing the moles of Na2SO4 by the mass of the solvent (H2O) in kilograms:
mass of H2O = 45.0g = 45.0g / 1000 = 0.045 kg
molality (m) = moles of Na2SO4 / mass of H2O
Finally, substitute the given values into the colligative property equation and solve for i:
-3.82°C = i * 1.86°C/m * (moles of Na2SO4 / 0.045 kg)
Solving for i, we get:
i = (-3.82°C) / (1.86°C/m * (moles of Na2SO4 / 0.045 kg))
Plug in the calculated values from above to get the value of the van't Hoff factor (i).