Use the law limit of Debye-Huckel and calculate the average activity coefficient for a solution of NaCl 0.050 mol/kg
To calculate the average activity coefficient using the law limit of Debye-Huckel, you need to gather some information. Here are the steps to follow:
Step 1: Collect the necessary information.
- Ionic strength of the solution (μ): It represents the total concentration of ions in solution and is calculated using the formula: μ = 1/2 ∑(zi^2ci), where zi is the charge number of each ion and ci is its molar concentration.
- Debye-Huckel limiting law constant (A): Its value depends on the temperature and dielectric constant of the solvent you are using. For water at 25°C, A is approximately 0.509 mol^(-1/2)L^(1/2).
- Valence of the ions (zi): Sodium (Na+) has a valence of +1, while chloride (Cl-) has a valence of -1.
- Molar concentration of NaCl (c): In this case, it is given as 0.050 mol/kg.
Step 2: Calculate the ionic strength (μ) of the solution.
In this case, since we have NaCl, and both ions have the same concentration, we can calculate μ as follows:
μ = 1/2 (1^2(0.050) + 1^2(0.050)) = 0.005 mol/kg.
Step 3: Calculate the average activity coefficient (γ±) using the Debye-Huckel limiting law.
The Debye-Huckel limiting law states that:
logγ± = -Az²√(μ) / (1 + B√(μ))
The value of B depends on the solvent and temperature. For water at 25°C, B is approximately 1.824.
Let's calculate γ±:
logγ± = -0.509 × (1²)√(0.005) / (1 + 1.824√(0.005))
logγ± ≈ -0.255
Taking the antilog (base 10) of both sides:
γ± ≈ 0.566
Thus, the average activity coefficient (γ±) for a solution of NaCl with a molar concentration of 0.050 mol/kg is approximately 0.566.