An electrochemical cell consists of a nickel metal electrode immersed in a solution with [Ni2+] = 1.0 M separated by a porous disk from an aluminium metal electrode immersed in a solution with [Al3+] = 1.0 M. Sodium hydroxide is added to the aluminium compartment causing Al(OH)3(s) to precipitate. After precipitation of Al(OH)3 has ceased, the concentration of OH- is 1.0 . 10-4 M and the measured cell potential is 1.82 V. Calculate Ksp for Al(OH)3.
Please help me! thank you so much!
1.62 x 10^-33
To calculate the solubility product constant (Ksp) for Al(OH)3, we will use the Nernst equation and the balanced equation for the precipitation reaction.
The balanced equation for the precipitation of Al(OH)3 is:
Al3+ + 3OH- → Al(OH)3
Here are the steps to calculate Ksp:
Step 1: Write the balanced equation for the cell reaction.
The cell reaction can be written as:
Ni(s) + 2Ni2+ → 2Ni3+
Step 2: Determine the cell potential (E°cell).
The cell potential is given as 1.82 V.
Step 3: Calculate the Nernst potential (Ecell) using the Nernst equation.
The Nernst equation is given as:
Ecell = E°cell - (RT/nF) * ln(Q)
Where:
Ecell is the cell potential (1.82 V)
E°cell is the standard cell potential (unknown)
R is the gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
n is the number of electrons transferred in the balanced equation (2)
F is Faraday's constant (96485 C/mol)
Q is the reaction quotient
Step 4: Calculate the reaction quotient (Q).
The reaction quotient can be calculated using the concentrations of the species involved in the precipitation reaction.
Q = [Al3+] * [OH-]^3
Given: [Al3+] = 1.0 M and [OH-] = 1.0 × 10^-4 M
Step 5: Substitute the values into the Nernst equation and solve for E°cell.
1.82 V = E°cell - (8.314 J/(mol·K)) * (298 K) / (2 mol) * ln(Q)
Step 6: Calculate Ksp using the cell potential.
Ksp = e^(nF * E°cell / (RT))
Given:
n = 1 (since 1 mole of Al(OH)3 is formed)
T = 298 K
Substitute the values into the equation:
Ksp = e^((1 mol) * (96485 C/mol) * E°cell / ((8.314 J/(mol·K)) * (298 K)))
Simplified:
Ksp = e^(0.1226 E°cell)
Step 7: Substitute the calculated value of E°cell into the equation and calculate Ksp.
Ksp = e^(0.1226 * 1.82)
Ksp ≈ e^0.224
Ksp ≈ 1.251
Therefore, the solubility product constant (Ksp) for Al(OH)3 is approximately 1.251.
To calculate the Ksp (solubility product constant) for Al(OH)3, we need to use the given information and apply the Nernst equation. Here's how to proceed:
Step 1: Write the balanced equation for the precipitation reaction of Al(OH)3:
Al^3+ + 3OH^- -> Al(OH)3(s)
Step 2: Determine the cell reaction from the electrochemical cell setup:
Al(s) + 3OH^- -> Al(OH)3(s)
Step 3: Use the given concentration of OH^- and the measured cell potential to find the standard cell potential (E°):
[OH^-] = 1.0 x 10^-4 M
Ecell = 1.82 V
Step 4: Apply the Nernst equation to relate the cell potential to the standard potential and concentration:
Ecell = E° - (RT/nF) lnQ
Since this is a solid-state reaction, the equilibrium expression (Q) can be written as:
Q = [Al(OH)3]
Step 5: Solve for E°:
1.82 V = E° - (RT/nF) ln[Al(OH)3]
Step 6: Calculate the value of ln[Al(OH)3]:
ln[Al(OH)3] = (E° - Ecell) / (RT/nF)
Substituting the appropriate values:
ln[Al(OH)3] = (E° - 1.82 V) / (RT/nF)
Step 7: Convert the natural logarithm to the exponential form:
[Al(OH)3] = e^[(E° - 1.82 V) / (RT/nF)]
Step 8: Calculate the value of Ksp by substituting the appropriate constants:
Ksp = [Al(OH)3]^3 = e^[(3E° - 3(1.82 V)) / (RT/nF)]
The constant values you need are:
R = 8.314 J/(mol·K) (gas constant)
T = temperature in Kelvin (should be specified in the question)
n = number of moles of electrons transferred (in this case, 3)
F = Faraday constant = 96485 C/mol (units of charge per mole of electrons)
By plugging in the proper values of R, T, E°, and solving the equation, you can calculate the Ksp for Al(OH)3.
1. Find the the standard cell potential of the initial Al-Ni electrochemical cell (before the addition of NaOH). Consult your General Chemistry textbook on how to do this.
2. The solubility equilibrium is:
Al(OH)3(s) <=>Al^3+(aq) + 3OH-(aq)
Ksp = [Al+3][OH]^3
[OH-](eq) = 1.0x10^-4 (given)
[Al+3](eq) = ____? (see below)
3. The electrochemical reaction is:
2Al(s) + 3Ni^+2(aq) ---> 2Al^+3(aq) + 3Ni(s)
According to the Nernst Equation,
E(cell) = Eo - [(0.0592)/n)]log{[Al+3]/[Ni+2]}
E(cell) is given, Eo you calculate, n = 3 electrons for Al, and [Ni+2] is given. Solve for [Al+3].
Substitute into the expression for the Ksp.
4. Look up the Ksp for Al(OH)3 and see if your answer has the correct power of 10. If it does, your calculations should be OK.