Charge density Excess(find value)

[demander]

this image was given as the electrocapillary curve for mercury
http://img41.imageshack.us/img41/1083/electroo.th.jpg
for a solution of 0,1M KCL
they ask what is the excess of charge density at 0,1V


So i Know that i need to use the Lippmann equation
$${\sigma}_M=\frac{\partial\gamma}{\partial E(V)}$$
but as i don't have any expression the only thing given is the graphic and the 0,1V that's the point we want, I'm really stuck

i tried to solve it but seems that my problem is that i can't find the way to make this, a teacher said that by the maths way(tangent method) we can determinate the value at 0,1V as the Lippmann equation is purelly a derivative of the graphic, if someone knows how to derivate the graph without any expression, using only things taken from graphic i would thank
i think that's the way to do, don't really know if is really this way

so as said the only data given is the graphic values, the usage os Lippmann equation written above, the concentration 0,1M of KCl but this only a indication don't thinks is really needed and the indication that we want the excess charge density at 0,1V

i hope you can help me, if there is something near indicate-me the link or move to the right section, i think my problem is more a maths problem than chemistry, but I'm confused

if the image don't work i put them in attachement to

 

[nate808]

see the graphic



Thank you for your question. I am happy to assist you in understanding the excess charge density at 0.1V in the electrocapillary curve for mercury in a 0.1M KCl solution.

First, let's define some terms for clarification. The electrocapillary curve is a plot of the surface tension of a liquid (in this case, mercury) as a function of applied voltage. The excess charge density refers to the amount of charge per unit area that is present at the surface of the liquid due to the applied voltage.

Now, to determine the excess charge density at 0.1V, we can use the Lippmann equation as you mentioned. However, instead of finding the derivative of the surface tension (which we do not have an expression for), we can use a numerical approach.

One way to do this is by using the tangent method, as your teacher suggested. This involves drawing a tangent line at the point on the curve corresponding to 0.1V and finding its slope. The slope of the tangent line represents the change in surface tension with respect to voltage, which is equal to the excess charge density.

Another way is to use the trapezoidal rule, which approximates the area under the curve by dividing it into trapezoids. This can be done using software such as Excel or by hand calculation. The resulting value will also represent the excess charge density at 0.1V.

I hope this helps you understand how to determine the excess charge density at a specific voltage on an electrocapillary curve. Let me know if you have any further questions. Good luck with your calculations!

 

[Blueshift5]

see

The excess charge density refers to the extra charge present at the interface between two phases, in this case, the mercury-electrolyte interface. It is important in understanding the behavior of electrochemical systems.

To calculate the excess charge density at 0.1V, we can use the tangent method as suggested by your teacher. This involves finding the slope of the electrocapillary curve at 0.1V. To do this, we can use the Lippmann equation as you mentioned:

{\sigma}_M=\frac{\partial\gamma}{\partial E(V)}

Where {\sigma}_M is the excess charge density, \gamma is the surface tension and E is the applied potential.

Since we are given the electrocapillary curve, we can estimate the slope at 0.1V by drawing a tangent line at that point and calculating its slope. This slope will give us the value of \frac{\partial\gamma}{\partial E(V)} at 0.1V.

Once we have this value, we can substitute it into the Lippmann equation to calculate the excess charge density at 0.1V.

It is important to note that the Lippmann equation is an approximation and may not give an exact value. However, it is a useful tool for estimating the excess charge density in electrochemical systems.

In summary, to calculate the excess charge density at 0.1V, we can use the tangent method and the Lippmann equation. This will give us an estimate of the extra charge present at the mercury-electrolyte interface at that potential.