Using the reaction and the E∘ given below
2Co^3+(aq)+2Cl^−(aq)→2Co^2+(aq)+Cl2(g)
E∘=0.46 V
what is the cell potential at 25 ∘C if the concentration are
[Co^3+]= 0.565M ,
[Co^2+]= 0.554M ,
and [Cl^−]= 0.838M
and the pressure of Cl2 is PCl2= 8.50atm ?
Express your answer numerically in volts.
I know I'm suppose to use the equation
E=E∘-(0.0591/n)logQ
but I'm not really sure how I'm suppose to find the moles of electron (n) and Q. Also, I'm not really sure what I should do with the pressure of Cl2.
Thanks in Advance!
2Co^3+ goes to 2Co^2+ so that changes by 2e. To check that, 2Cl^- goes to Cl2 and that's a change of 2e. So n = 2.
Q = (Co^2+)^2*pCl2)/(Co^3+)^2(Cl^-)^2
Just plug in the numbers for Q. For pCl2, plug in 8.50 atm.
Thank you so much, it makes a lot more sense now! :)
To solve this problem, you're on the right track with using the Nernst equation, which is:
E = E° - (0.0591/n)log(Q)
Where:
E is the cell potential at 25°C,
E° is the standard cell potential,
n is the number of moles of electrons transferred in the balanced reaction, and
Q is the reaction quotient.
Let's break down the problem step by step to find n and Q.
1. Balanced equation:
The balanced equation given is:
2Co^3+(aq) + 2Cl^-(aq) → 2Co^2+(aq) + Cl2(g)
From the equation, you can see that 2 moles of electrons are transferred for every 2 moles of Co^3+ reduced.
Therefore, n = 2 (the number of moles of electrons transferred in the balanced equation).
2. Calculate Q:
To calculate Q, you can use the concentrations of the reactants and products as follows:
Q = ([Co^2+]^2 x [Cl2]) / ([Co^3+]^2 x [Cl^-]^2)
Plugging in the given values:
Q = (0.554^2 x 8.50) / (0.565^2 x 0.838^2)
3. Dealing with the Cl2 pressure:
Since Cl2 is in the gas phase, its concentration does not affect Q directly. However, we need to consider the pressure (PCl2) to determine the partial pressure of Cl2 in the reaction.
Assuming ideal gas behavior, we can use the ideal gas law to calculate the partial pressure of Cl2:
PCl2 = [Cl2] x R x T
Where:
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature in Kelvin (25°C = 25 + 273.15 = 298.15 K).
Plugging in the given values:
PCl2 = 8.50 atm x 0.0821 L·atm/(mol·K) x 298.15 K
4. Calculate E:
Now, you have all the values needed to calculate E using the Nernst equation:
E = E° - (0.0591/n)log(Q)
Plug in the given values and solve for E:
E = 0.46 V - (0.0591/2)log(Q)
Remember to use logarithm base 10 for the log function.
That's it! Now you have the step-by-step process to find the cell potential at 25°C. Let me know if you have any further questions.