Calculate the concentration of an unknown solution in a...

Calculate the concentration of an unknown solution in a concentration cell. A concentration cell consisting of two hydrogen electrodes ($P_{H_2} = 1 atm$), where the cathode is a standard hydrogen electrode and the anode solution has an unknown pH, has a cell voltage of 0.181 V. What is the pH in the unknown solution? Assume the temperature of the solutions is 298 K. $pH = \text{____}$

Transcript

00:01 The non -standard cell potential can be computed using the nernst equation which we write as e equals the standard cell potential and the temperature equals 298 kelvin.

00:19 We have the form of formula e equals e standard cell minus 0 .0592 divided by n then multiplied by the log of q where n is the number of electrons transferred, q is the reaction quotient and e cell standard is the standard cell potential.

00:45 So first we're going to establish the overall equation so that we can know the e cell as well as the number of electrons transferred.

00:53 So here we have a concentration cell with two hydrogen electrodes so that means you have the same electrodes on the two compartments.

01:03 We have reduction half reaction for a hydrogen cell or a hydrogen cell yes to be 2h plus plus two electrons to form h2 gas and also this is the same as the oxidation only reversed that is h2 to form 2h plus plus two electrons.

01:26 So since this is the reference or this is the standard hydrogen electrode and this is the reference cell we call both the reduction potential for these half reactions would be equal to zero.

01:46 So once again because this is the she, the standard hydrogen electrode which is the reference for the reduction potential.

01:55 So we find here that the number of electrons transferred is two since the reduction potential value is zero for both half reactions then overall the cell potential at standard condition will also be zero.

02:08 Now to get the overall equation we're going to add the two equations giving us 2h.

02:18 Moreover it is important that it is given that the cathode is a standard hydrogen electrode.

02:24 So is that corrected? the only standard hydrogen electrode here should have been this cathode the one that there is a standard there is reduction going on.

02:35 So that means the concentration of hydrogen ion here is going to be one molar the pressure of the h2 will be one atm.

02:49 Pressure for the hydrogen gas in the oxidation half reaction is one atm but we don't know what the concentration of hydrogen ion in the cathode or or rather in the anode half or in the anode compartment.

03:03 So that we will find from this problem...

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