2) Calculate the following properties of 2,4,6-trichlorophenol (C6H3Cl3O) at 25ºC:
- Diffusion coefficient in water (cm2/s)
- Henry’s constant [(atm·m3)/mol]
- Henry’s constant (dimensionless)
Given information:
- Universal gas constant (R) = 0.082 atm·L/mol·°K
- Viscosity of water at 25ºC = 0.89 cP
- Partial pressure of 2,4,6-trichlorophenol = 0.6 × 10-2 mmHg when 197.5 g is placed in a closed container along with 197.5 g of 2,4,5-trichlorophenol
- Water solubility of 2,4,6-trichlorophenol = 800 mg/L
- Atomic weights of C, H, Cl, and O are 12, 1, 35.5, and 16, respectively
To calculate the diffusion coefficient in water, Henry's constant in (atm·m3)/mol, and Henry's constant dimensionless for 2,4,6-trichlorophenol at 25ºC, we need to follow these steps:
1. Convert the given partial pressure of 2,4,6-trichlorophenol from mmHg to atm:
- Given partial pressure = 0.6 × 10^(-2) mmHg
- Conversion: 1 mmHg = 0.00131578947 atm
- Partial pressure in atm = 0.6 × 10^(-2) mmHg * 0.00131578947 atm/mmHg
2. Calculate the molarity of 2,4,6-trichlorophenol in water:
- Given water solubility = 800 mg/L
- Conversion: 1 mg/L = 1 mg/1000 mL = 1 mg/0.001 L
- Solubility in g/L = 800 mg/L * (1 g/1000 mg)
- Molarity = (Solubility in g/L) / Molecular weight of 2,4,6-trichlorophenol
3. Calculate the concentration in mol/L:
- Concentration = Molarity / 1000
4. Calculate the Henry's constant in (atm·m3)/mol:
- Henry's constant = (partial pressure in atm) / (concentration in mol/L)
5. Calculate the Henry's constant dimensionless:
- Henry's constant (dimensionless) = Henry's constant * (universal gas constant / 0.082)
6. Finally, calculate the diffusion coefficient in water using the Stokes-Einstein equation:
- Diffusion coefficient = (universal gas constant * temperature) / (6 * π * viscosity * hydrodynamic radius)
Note: The hydrodynamic radius can be estimated using the molecular weight and assuming the molecule to be spherical.
By following these steps and plugging in the given values, you should be able to calculate the properties of 2,4,6-trichlorophenol at 25ºC.