What is the ionic strength, I, of a solution at 25C containing 0.002 mol/L of BaSO4 and 0.001 mol/L of BaCl2? What is the activity coefficient of Ba2+ in this solution?
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0.081
To calculate the ionic strength (I) of a solution, you need to determine the sum of the concentrations of all ions in the solution.
In this case, you have two ions: Ba2+ and Cl-. The concentration of Ba2+ in the solution is 0.002 mol/L (from BaSO4) and 0.001 mol/L (from BaCl2). The concentration of Cl- in the solution is 0.001 mol/L (from BaCl2).
The ionic strength (I) can be calculated using the formula:
I = 1/2 * [sum of (concentration of ion * square of its charge)]
For Ba2+, the charge is +2, and we have a concentration of 0.002 mol/L. So, the contribution of Ba2+ to the ionic strength is:
0.002 mol/L * (2^2) = 0.008 mol/L.
For Cl-, the charge is -1, and we have a concentration of 0.001 mol/L. So, the contribution of Cl- to the ionic strength is:
0.001 mol/L * (1^2) = 0.001 mol/L.
Now, we can calculate the total ionic strength by summing the contributions of Ba2+ and Cl-:
I = 0.008 mol/L + 0.001 mol/L
I = 0.009 mol/L.
Therefore, the ionic strength (I) of the solution is 0.009 mol/L.
To calculate the activity coefficient (γ) of Ba2+ in this solution, we need to use the Debye-Hückel equation:
log(γ) = -0.51 * (z^2 * I^0.5) / (√(1 + α * I^0.5))
Where:
- γ is the activity coefficient
- z is the charge of the ion (in this case, +2 for Ba2+)
- I is the ionic strength
- α is the ionic strength coefficient (approximately 0.5 for Ba2+ and Cl-)
Plugging in the values:
log(γ) = -0.51 * (2^2 * 0.009^0.5) / (√(1 + 0.5 * 0.009^0.5))
Simplifying the equation:
log(γ) = -0.51 * (4 * 0.009^0.5) / (√(1 + 0.5 * 0.009^0.5))
Using a calculator to evaluate the expression inside the log and the square root:
log(γ) = -0.51 * (4 * 0.03) / (√(1 + 0.015))
log(γ) = -0.51 * 0.12 / (√(1.015))
log(γ) = -0.0612 / (1.007)
log(γ) = -0.0609
Taking the antilog of both sides:
γ = 10^(-0.0609)
γ ≈ 0.941
Therefore, the activity coefficient (γ) of Ba2+ in this solution is approximately 0.941.
To calculate the ionic strength (I) of a solution, you need to consider the concentration of all the ions present.
In this case, the solution contains 0.002 mol/L of BaSO4 and 0.001 mol/L of BaCl2.
1. First, calculate the contribution of each ion to the ionic strength:
- BaSO4 dissociates into Ba2+ and SO42-. So, the contribution of Ba2+ ions is 0.002 mol/L.
- BaCl2 dissociates into Ba2+ and 2 Cl- ions. So, the contribution of Ba2+ ions from BaCl2 is 0.001 mol/L.
2. Sum up the contributions of all ions:
- Ba2+ contribution = 0.002 mol/L (from BaSO4) + 0.001 mol/L (from BaCl2) = 0.003 mol/L
3. The ionic strength (I) is calculated using the formula:
I = 1/2 * [Σ (ci * zi^2)]
Where:
- ci is the concentration of each ion
- zi is the charge of each ion
In this case, since we are only considering the contribution of Ba2+, we have:
I = 1/2 * [(0.003 mol/L) * (2^2)] = 0.003 mol/L
The ionic strength of the solution is 0.003 mol/L.
To calculate the activity coefficient (γ) of Ba2+ in the solution, you can use an activity coefficient model such as the Debye-Hückel equation. The Debye-Hückel equation approximates the activity coefficient for dilute solutions:
γ = 10^(-A * (z1 * z2 * √(I))/(√(2) * RT))
Where:
- A is the Debye-Hückel constant, typically around 0.509 mol^(-1/2) L^(1/2)
- z1 and z2 are the charges of the ions involved (in this case, Ba2+ has a charge of +2)
- I is the ionic strength (calculated as 0.003 mol/L)
- R is the ideal gas constant (8.314 J/(mol*K))
- T is the temperature in Kelvin (25°C = 298 K)
Plugging in the values, we get:
γ = 10^(-0.509 * (2 * √(0.003))/(√(2) * 8.314 * 298))
Calculating this using a calculator, the activity coefficient of Ba2+ in the solution is approximately 0.906.