A cell has a standard cell potential of +0.177 V at 298 K. What is the value of the equilibrium constant for the reaction

(a) if n = 1?

Video transcript

All right. Hello everyone. So this question says that a cell produces 1.10 volts at 298. Kelvin determine the equilibrium constant for the reaction happening inside. If the cell is N equals one here, we have four different entry choices labeled A through D proposing different values for the equilibrium constant. So in this particular question, we have to use information regarding the cell potential to calculate the equilibrium concept. This means that the reaction in question is going to be as follows in which the e standard of the cell is equal to RT divided by NF multiplied by the Ln of K K is the equilibrium constant. R is the gas constant T is temperature and is the number of moles and F is Faraday constant. But before you go ahead and recall those values for these variables here, let's go ahead and rearrange this equation to isolate what it is we're solving for because we're solving for the equilibrium constant. The idea is to first isolate this term here, which is the Ln of K. So to do so, first and foremost, let's go ahead and multiply both sides of this equation by NF. And by doing so we get that RT multiplied by the Ln of K is equal to E standard of the. So multiplied by NF from here, we can divide both sides of the equation by RT. And so the Ln of K is equal to NF multiplied by E standard of the cell divided by RT. And so this is the equation that we're going to use because now K which is what we're solving for is on one side of the equation. So now let's recall the values for these constants. First off, we have F which is Faraday constant and that's equal to 96,485 cool Los pol R is the gas constant and that's equal to 8.314 jules, PMO Kelvin. And so from here, we can go ahead and plug in the information provided to us in the text of the question because our temperature which is T is equal to 298. Kelvin N is equal to one and each standard of the cell has been provided to us because E standard of the cell which is the standard potential is equal to 1.10 volts or 1.10 joules per kilo. So from here, let's go ahead and solve for the Ln of K. So here in the numerator, we have N multiplied by F multiplied by the cell potential. So N is equal to one multiplied by the value of F which is 96,485 coons per month. I should specify that, that the uniter and his moles. So that's Faraday constant multiplied by one mole and multiplied by the self potential which was 1.10 jules per kilo. All of this is divided by the denominator which is or multiple by T R is 8.314 jewels per mole. Kelvin and tea is 298 Kelvin. And so from here, keep in mind that all units are going to cancel out, which does make sense considering the equilibrium constant does not have any units associated to it. And so after evaluating this expression, the Ln of K is equal to 42.8377 0562. And so I'm using the ungrounded value because now we're going to convert the Ln of K into the actual equilibrium constant using the properties of logarithms. We can go ahead and cancel out the Ln here. So here K is equal to E to the power of that 42.8377 0562. So from here we evaluate once more and K is equal to 4.01956 multiplied by 10 to the 18th power. So here rounding our value for K to three significant figures gives us our final answer, which is 4.02 multiplied by 10 to the power of 18. And there you have it. So the value of the equilibrium constant for this reaction is 4.02 multiplied by 10 to the power of 18, which corresponds to option B in the multiple choice. And so with that being said, thank you so very much for watching. And I hope you found this helpful.