A voltaic cell consists of a standard hydrogen electrode in one half-cell and a Cu/Cu2+ half-cell. Calculate [Cu2+] when E cell is 0.22 V.
Cu^2+ + 2e ==> Cu Eo = 0.337 v
H2 ==> 2H^+ 2e Eo = 0.00 v
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Cu^2+ + H2 ==> Cu(s) + 2H^+ EoCell = 0.337
Ecell = 0.22 v
Ecell = Eocell - (0.0592/2) log Q
Plug in 0.22 for Ecell and 0.337 for Eocell and solve for Q for the reaction.
Then Qrxn = [Cu(s)][(H^+)^2]/[(Cu^2+)][H2]
Cu(s) is 1; (H^+)^2 is 1; (H2) in the denominator is 1 and Cu^2+ is the unknown. Solve for that. The unknown concn Cu^2+ should be less than 1 M
I obtained about 1E-4 but that's just a close estimate.
Post your work if you get stuck.
The answer I get is 0.0 for Cu^2+. Is that correct
0,99
Ah, the wonderful world of voltaic cells! Let me put on my electrifying thinking cap and give you an answer that will really shock you.
Now, in order to calculate [Cu2+], we need to use the Nernst equation, which goes like this:
E cell = E° cell - (0.0592/n) * log([Cu2+])
Where E cell is the cell potential, E° cell is the standard cell potential, [Cu2+] is the concentration of copper ions, and n is the number of electrons transferred in the half-reaction.
For this problem, we have an E cell of 0.22 V. But wait, before we can proceed, we need to know the value of E° cell for this particular reaction. Once we have that, we can plug it into the equation and solve for [Cu2+].
So, without further ado, let me balance on my unicycle to fetch you the standard cell potential value...
*Bot falls off unicycle*
Whoops! Looks like I lost my balance there. Okay, let's try again. *Bot hops back up on unicycle*
After some research, I've found that the standard cell potential for a Cu/Cu2+ half-cell is 0.34 V. Now, let's get back to our equation and plug in these values:
0.22 V = 0.34 V - (0.0592/n) * log([Cu2+])
Now, you'll need to do some algebraic magic to solve for [Cu2+]. Remember, with great algebraic power comes great responsibility!
Psst, if you need extra help with the calculations, just let me know. I'm here to clown around and assist you!
To calculate the concentration of Cu2+ in the Cu/Cu2+ half-cell, we can use the Nernst equation. The Nernst equation relates the cell potential (E cell) to the concentrations of the species involved in the redox reaction.
The general form of the Nernst equation is:
E cell = E° cell - (RT / nF) * ln(Q)
Where:
E cell = cell potential (in volts)
E° cell = cell potential under standard conditions (in volts)
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature (in Kelvin)
n = number of electrons transferred in the balanced equation
F = Faraday's constant = 96,485 C/mol
Q = reaction quotient
In this case, since E cell is given and we need to find [Cu2+], we rearrange the Nernst equation as follows:
E cell = E° cell - (RT / nF) * ln(Cu2+ / Cu)
Since the standard reduction potential of the Cu/Cu2+ half-cell is not given, we assume the standard hydrogen electrode (SHE) is at 0V. Hence, E° cell = 0 when the hydrogen electrode is the reference electrode.
Now, we substitute the given values and simplify the equation to solve for [Cu2+]:
0.22 V = 0 - (RT / 2F) * ln(Cu2+ / Cu)
Let's assume the temperature is 25°C (298 K) and simplify the equation further:
0.22 V = -(0.0257 V / 2) * ln(Cu2+ / Cu)
0.22 V = -0.01285 V * ln(Cu2+ / Cu)
To solve for [Cu2+], we rearrange the equation:
ln(Cu2+ / Cu) = 0.22 V / -0.01285 V
ln(Cu2+ / Cu) = -17.113
Now, we can take the exponential of both sides of the equation to eliminate the natural logarithm:
Cu2+ / Cu = e^(-17.113)
Finally, rearrange the equation to solve for [Cu2+] by multiplying both sides with Cu:
[Cu2+] = Cu * e^(-17.113)
Please provide the concentration of Cu (in moles per liter) in the Cu/Cu2+ half-cell, and you can calculate [Cu2+] using the equation above.