Calculate the unknown of Ag+ if the potential of the following concentration cell is 300 mV at 25.0 C.
Ag|Ag+(unknown)||Ag+(0.100M)|Ag
I think I have to use Nernst Equation of
Ecell=E0-.0592/nlogQ
And at 25C is at 298K so i don't have to change anything. I am not sure if i just plug everything in or not.
Thank you in advance
Thank you so much
To calculate the unknown concentration of Ag+, you can use the Nernst equation. Let's break it down step-by-step:
Step 1: Identify the key information given in the problem:
- The potential of the concentration cell (Ecell) is 300 mV.
- The temperature (T) is 25.0 °C (which can be directly used as 298 K).
- The cell is set up as: Ag|Ag+(unknown)||Ag+(0.100M)|Ag.
Step 2: Determine the balanced redox equation:
The cell is set up with Ag and Ag+ on both sides, which indicates the reduction of Ag+ to Ag. The balanced equation is: Ag+ + e- -> Ag.
Step 3: Identify the number of electrons involved (n):
In the balanced equation above, one electron is involved in the reaction, so n = 1.
Step 4: Calculate the standard cell potential (E0):
You didn't provide the standard reduction potential (E0) for the Ag+/Ag half-reaction, but you can find it in a reference table or online. Let's assume the value is 0.80 V.
Step 5: Calculate the reaction quotient (Q):
The reaction quotient (Q) is the ratio of the concentrations of the products over the concentrations of the reactants. In this case, Q = [Ag+]unknown/[Ag+]0.100M. However, we don't have the value for [Ag+]unknown yet.
Step 6: Substitute the known values into the Nernst Equation:
With the information gathered so far, we can now use the Nernst equation to find the unknown concentration [Ag+]unknown:
Ecell = E0 - 0.0592/n * log(Q)
300 mV = 0.80 V - 0.0592/1 * log(Q)
Step 7: Solve for Q:
Rearrange the equation to solve for Q:
300 mV + 0.0592/1 * log(Q) = 0.80 V
0.0846 * log(Q) = 0.50 V
log(Q) ≈ 0.50 V / 0.0846
log(Q) ≈ 5.91
Q ≈ 10^5.91
Step 8: Calculate [Ag+]unknown:
Now that we have Q, we can substitute it into our equation:
Q = [Ag+]unknown/[Ag+]0.100M
10^5.91 = [Ag+]unknown / 0.100 M
Rearranging the equation:
[Ag+]unknown ≈ 10^5.91 * 0.100 M
[Ag+]unknown ≈ 7.94 M
Therefore, the approximate unknown concentration of Ag+ is 7.94 M.
To calculate the unknown concentration of Ag+ in the given concentration cell, you can use the Nernst equation. Here's how you can proceed:
1. Determine the given values:
- E_cell = 300 mV (potential of the concentration cell)
- T = 25.0°C = 298 K (temperature)
2. Identify the half-reactions happening at each electrode:
- At the left electrode (anode): Ag → Ag+ (unknown concentration)
- At the right electrode (cathode): Ag+ (0.100 M) → Ag
3. Determine the cell potential at standard conditions, E°:
- The standard potential for the half-reaction 2Ag+ + 2e- → 2Ag is 0.00 V. Therefore, E° = 0.00 V.
4. Calculate the reaction quotient, Q:
- Since the unknown concentration is on the anode side, Q would be the concentration of Ag+ at the cathode divided by the concentration of Ag+ at the anode:
Q = [Ag+]cathode / [Ag+]anode = (0.100 M) / [Ag+]anode
5. Substitute the given values into the Nernst equation:
- E_cell = E° - (0.0592 / n) * logQ
- Since the reaction involves the transfer of two electrons (2Ag+ + 2e- → 2Ag), n = 2 in this case.
Putting it all together, we have:
300 mV = 0.00 V - (0.0592 / 2) * log((0.100 M) / [Ag+]anode)
6. Rearrange the equation to solve for [Ag+]anode:
- First, multiply both sides by 2 to get rid of the fraction: 600 mV = -0.0592 * log((0.100 M) / [Ag+]anode)
- Divide both sides by -0.0592 to isolate the logarithm: log((0.100 M) / [Ag+]anode) = -600 mV / -0.0592
- Evaluate the right side: log((0.100 M) / [Ag+]anode) ≈ 10169
- Convert to exponential form: 10^10169 = (0.100 M) / [Ag+]anode
- Rearrange the equation to solve for [Ag+]anode: [Ag+]anode = (0.100 M) / 10^10169
Note: The resulting concentration [Ag+]anode is extremely small and practically almost negligible.
However, it is important to note that the Nernst equation assumes ideal conditions and does not take into account any side reactions or other effects. Therefore, the calculated concentration using this equation may not entirely reflect the real-world situation.
Ecell=E0-(.0592/n)logQ
Eo is 0
0.3 = -0.0592*log Q
Solve for Q. Then
Q = (dilution solution)/(concentrated solution)
You have no way of knowing which the the more dilute but you can try it both ways; i.e. substitute Q and 0.1 and try it.
Q = 0.1/x and Q = x/0.1. One of the answers will not be realistic so you take the other one.