# Nernst Equation Experiment

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Hi,

I am a secondary school student from England looking into advanced chemistry. I have been learning about the nernst equation and am planning an experiment on this topic. I need to measure a change of 0.001 volts (a milivolt) with a starting voltage of 1V. How can I do this, my school has a multi-meter however its milivolt reader only has 3 significant figures (up to 99.9 mV). At 1.001 volts   I would need up to 9999 mV.

Find attached proposed experiment

Thanks

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There are several ways to overcome this.

Your Science department may have a sensitive enough oscilloscope to make the measurement.

Or you could use a couple of high value resistors in a potential divider arrangement to scale the output down to be within the range of your multimeter

Please note the spelling of meter when referring to a measuring instrument.

Or you could use you multimeter as a detector in a null measurement by potentiometric means.
This is an old fashioned way.

Congratulations on the attempt, I don't remember Nernst being even in the old Scholarship level syllabus, let alone the A level.

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Fortunately Electromagnetism is what Physicist call a gauge force.
In simple terms that means there is no absolute value for voltage ( like, say, for temperature ), and if you use 1V as your reference, you will be able to measure +/_ 0.001 V on either side of it.

Edited by MigL

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9 hours ago, studiot said:

There are several ways to overcome this.

Your Science department may have a sensitive enough oscilloscope to make the measurement.

Or you could use a couple of high value resistors in a potential divider arrangement to scale the output down to be within the range of your multimeter

Please note the spelling of meter when referring to a measuring instrument.

Or you could use you multimeter as a detector in a null measurement by potentiometric means.
This is an old fashioned way.

Congratulations on the attempt, I don't remember Nernst being even in the old Scholarship level syllabus, let alone the A level.

A potential divider is probably my best bet. My multimeter can go down to a 10th of a milivolt. Should I use a resister setup of 1000:1 or of 10000:1?

The Nernst equation is not on the A-level specification, it is my own work.

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24 minutes ago, Harry_- said:

A potential divider is probably my best bet. My multimeter can go down to a 10th of a milivolt. Should I use a resister setup of 1000:1 or of 10000:1?

The Nernst equation is not on the A-level specification, it is my own work.

That depends upon what resources you have available and your knowledge of electric circuit theory.

Perhaps that could be incorporated?

If you go for a second potential divider across that it wil need to be at least an order of magnitude higher resistance than your high value resistor.

Have you studied corrections for parallel value voltage measurements?

Edited by studiot

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This is also a good opportunity to consider measuring accuracy and what can be achieved.

Since you want to study Nernst, you will presumably want to measure the potential at different temperatures and/or concentration?

This you can do to a greater precision than you can achieve in terms of absolute accuracy.

In other words your meter and setup might read 1.017 V and change to 1.031 V

Neither of these will be absolutely correct, but their difference will be.

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OK so after talking through with a few teachers we believe a potential divider won't work and the reasoning is this:

Say we had 1000:1 . Our 1000 ohm would give 1.0044 V and our 1 ohm would read 0.0010044 and therefor we would never be able to read that on my equipment.

Potentiometric voltmeters require precise resistors whereas the ones I have available have 10% error.

As for circuit theory I have looked into potential dividers and resistors in series and parallel but not much else.

My plan for now is to try and talk to the local university and see if they have any equipment I could use or get lab time.

If you think of any other possible options, I will be here.

Thanks

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19 hours ago, MigL said:

Fortunately Electromagnetism is what Physicist call a gauge force.
In simple terms that means there is no absolute value for voltage ( like, say, for temperature ), and if you use 1V as your reference, you will be able to measure +/_ 0.001 V on either side of it.

That's unequivocally true, but I wonder if the OP can make use of it.

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2 hours ago, Harry_- said:

OK so after talking through with a few teachers we believe a potential divider won't work and the reasoning is this:

Say we had 1000:1 . Our 1000 ohm would give 1.0044 V and our 1 ohm would read 0.0010044 and therefor we would never be able to read that on my equipment.

Potentiometric voltmeters require precise resistors whereas the ones I have available have 10% error.

As for circuit theory I have looked into potential dividers and resistors in series and parallel but not much else.

My plan for now is to try and talk to the local university and see if they have any equipment I could use or get lab time.

If you think of any other possible options, I will be here.

Thanks

'Potentiometric' is not the same as using a potential divider!

I am unclear as to your intended purpose and aim of the experiment.

As I understand it you are seeking to measure the change of cell EMF when concentration is changed (and presumably other factors are held constant)

But you are limited by the resolution of your voltmeter, only the most sensitive scale will offer millivolt resolution.

Since change is not an absolute measurement that is within the capacity of your experiment, with suitable reference voltage, as MigL and I have said.
That is the potentiometric method.  -Balancing one voltage against another.

But you should understand there is no way a school (or even a quite sophisticated lab) could expect to control the variables in the Nernst equation to obtain the precision of absolute voltage measurement your document is quoting.

Who wrote it?

Note even only having 10% resistors (pretty poor these days) can be overcome by selection.

You can use your meter and a battery or other voltage source to set a divider to meet the maximum resolution of your meter by selecting resistors.

Edited by studiot

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Applying an extremely well regulated ( to 3 dec. places ) power supply to the 'ground' or common ( black lead ) on your digital multimeter, you will then be able to measure to 3 dec. places on either side of 1 V.
IOW the red lead will measure the difference ( positive or negative ) from the 1 V reference.

( I agree, a well regulated power supply would be more difficult to source than a multimeter that reads to 4 dec. places )

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13 hours ago, studiot said:

'Potentiometric' is not the same as using a potential divider!

I am unclear as to your intended purpose and aim of the experiment.

As I understand it you are seeking to measure the change of cell EMF when concentration is changed (and presumably other factors are held constant)

But you are limited by the resolution of your voltmeter, only the most sensitive scale will offer millivolt resolution.

Since change is not an absolute measurement that is within the capacity of your experiment, with suitable reference voltage, as MigL and I have said.
That is the potentiometric method.  -Balancing one voltage against another.

But you should understand there is no way a school (or even a quite sophisticated lab) could expect to control the variables in the Nernst equation to obtain the precision of absolute voltage measurement your document is quoting.

Who wrote it?

Note even only having 10% resistors (pretty poor these days) can be overcome by selection.

You can use your meter and a battery or other voltage source to set a divider to meet the maximum resolution of your meter by selecting resistors.

The aim of the experiment is to look into the effect of change of concentration of electrolyte on cell voltage. This is to help me test the nernst equation. The document was written by me and I have no hope of recording to such precise values however I do want at least milivolts. I understand my values will not be completely correct, the point is to test the equation, not get exact values.

I have been given an electrometer by the university. With resolution 100 micro volts and going up to 2V I should be able to obtain values from this.

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1 hour ago, Harry_- said:

The aim of the experiment is to look into the effect of change of concentration of electrolyte on cell voltage. This is to help me test the nernst equation. The document was written by me and I have no hope of recording to such precise values however I do want at least milivolts. I understand my values will not be completely correct, the point is to test the equation, not get exact values.

I have been given an electrometer by the university. With resolution 100 micro volts and going up to 2V I should be able to obtain values from this.

I am pleased that you will now be able to concentrate on the physical chemistry rather than the electronics.

So it is now appropriate to consider the challenges in what you are attempting.

Firstly the Nernst equation depends upon temperature.
The chemical action involved will change that.
This is separate from any electrical heating due to the curent drawn, which you will minimise by restricting the current using a high value resistor.
How will you measure the temperature and what accuracy will you require to obtain millivolt precision in your calculation?

Then there is the question of the value of the temperature.
Nernst assumes that the whole of the body of both solutions is at the same temperature and guaranteeing that, to one millivolt is no small order.

Then there is also the question of the accuracy of your concentrations.
Because of the difficulty in obtaining accuracy with small quantities when weighing out and transferring etc pharmacists, for instance, often make up far too much by a factor 10, 100 or even 1000 and dilute the solution by these factors.
This reduces the errors.

These are the chemical difficulties I can think of.

But there are also physical ones in measuring at or below the millivolt level.

One is contact potentials between connections and sections of the wiring.
Another is surface leakage when measuring at high resistance.
Another might be random radio pickup or noise from your 10% resistors.

The use of electrometers in physical chemistry is often accompanied by 'guard rings'.

If you go on to do much electrochemistry these considerations will become commonplace for you (as will electrometers).

Go well and let us know how you get on.

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5 hours ago, studiot said:

I am pleased that you will now be able to concentrate on the physical chemistry rather than the electronics.

So it is now appropriate to consider the challenges in what you are attempting.

Firstly the Nernst equation depends upon temperature.
The chemical action involved will change that.
This is separate from any electrical heating due to the curent drawn, which you will minimise by restricting the current using a high value resistor.
How will you measure the temperature and what accuracy will you require to obtain millivolt precision in your calculation?

Then there is the question of the value of the temperature.
Nernst assumes that the whole of the body of both solutions is at the same temperature and guaranteeing that, to one millivolt is no small order.

Then there is also the question of the accuracy of your concentrations.
Because of the difficulty in obtaining accuracy with small quantities when weighing out and transferring etc pharmacists, for instance, often make up far too much by a factor 10, 100 or even 1000 and dilute the solution by these factors.
This reduces the errors.

These are the chemical difficulties I can think of.

But there are also physical ones in measuring at or below the millivolt level.

One is contact potentials between connections and sections of the wiring.
Another is surface leakage when measuring at high resistance.
Another might be random radio pickup or noise from your 10% resistors.

The use of electrometers in physical chemistry is often accompanied by 'guard rings'.

If you go on to do much electrochemistry these considerations will become commonplace for you (as will electrometers).

Go well and let us know how you get on.

I am also happy to get away from the electronics :)

As for temperature, my maximum resolution is 0.1 kelvin due to equipment av available. Obviously this isn't ideal with my level of precision of voltage but without that precision I wouldn't see any change in voltage and therefore would have no results to show.

As for concentration I believe the school's are 5% error, which again isn't great but it will have to do. Unfortunately waste will not be accepted by my teachers and they don't want several dm(3) of solution lying around. I will try and make as large quantities as they will allow (probably 250cm(3) for each electrolyte), using a volumetric flask.

Your physical problems are very interesting and I have never come across any of them before. I theorise with random radio pickup I may have fluctuating values of milivolts and therefore I should take an average of these. As for the other two, I do not believe there is much I can do to minimise these with the equipment I have (and with the level of accuracy I have will these matter?). Nevertheless you have given me many topics which sound fascinating and I will look into contact potentials especially.

As for results, I cannot hope to get completely theoretical values due to systematic errors such as concentration and resistance. However as they are systematic, although my graph my have a slightly incorrect gradient and y-intercept, I should find a trend similar to that of the nernst equation.

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4 minutes ago, Harry_- said:

As for results, I cannot hope to get completely theoretical values due to systematic errors such as concentration and resistance. However as they are systematic, although my graph my have a slightly incorrect gradient and y-intercept, I should find a trend similar to that of the nernst equation.

Yes.

Please don't get me wrong I find your intentions and thinking very impressive and want to offer every encouragement. I definitely think you will get much useful out of this excercise. +1

All the difficulties I have outlined are for your further interest.

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18 hours ago, MigL said:

Applying an extremely well regulated ( to 3 dec. places ) power supply to the 'ground' or common ( black lead ) on your digital multimeter, you will then be able to measure to 3 dec. places on either side of 1 V.
IOW the red lead will measure the difference ( positive or negative ) from the 1 V reference.

( I agree, a well regulated power supply would be more difficult to source than a multimeter that reads to 4 dec. places )

Over the duration of a typical school experiment I suspect that a torch battery might be good enough. (A slightly used Hg cell will give you 1.35V- reliable to 3 sig fig over the course of a few years.)

Logically, you can set up two "sets" of whatever the experiment is; change one, and measure the difference.

If the first one isn't stable enough then the experiment's meaningless anyway.

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So... OK I got bored + wondered how stable a torch battery is.

I measured the voltage on my two bench multimeters over the afternoon. They both claim GOhm input impedances so they aren't drawing much current.

 12:40 1.59115 1.59121 12:52 1.59114 1.59118 13:40 1.59112 1.59113 14:15 1.5911 1.59108 15:56 1.59101 1.59095 16:45 1.5909 1.59083 17:55 1.59081 1.59073

I guess the biggest effect is a change in temperature as the room warms up over the course of the day.

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3 hours ago, John Cuthber said:

12:40 1.59115 1.59121 12:52 1.59114 1.59118 13:40 1.59112 1.59113 14:15 1.59110 1.59108 15:56 1.59101 1.59095 16:45 1.59090 1.59083 17:55 1.59081 1.59073

Pity your table won't quote, John.

The main thing to be seen in it is the uncanny temporal progression of the difference between the readings on the two meters.

12:40     +6

12:52     +4

13:40     +1

14:15      -2

15:56     -6

16:45     -7

17:55     -8

Edited by studiot

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Good work John.
Very satisfying to still get to do some 'sperimentin' at our age.

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I was wondering, why do batteries slowly run out over time? I presume in electronics such as a torch that the circuit is broken when unused so why does this occur?

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Well, here's the data, including that from later in the day

 12:40 1.59115 1.59121 12:52 1.59114 1.59118 13:40 1.59112 1.59113 14:15 1.5911 1.59108 15:56 1.59101 1.59095 16:45 1.5909 1.59083 17:55 1.59081 1.59073 19:25 1.59086 1.59077 20:30 1.59089 1.59081 22:00 1.59093 1.59085

And, as I said,  I suspect that temperature makes a difference.

It's plausible that one meter is better "lagged" than the other so there's a delay between them.

Neither meter is properly calibrated, but that hardly matters here.

I may get round to thermostating a torch battery.

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13 hours ago, Harry_- said:

I was wondering, why do batteries slowly run out over time? I presume in electronics such as a torch that the circuit is broken when unused so why does this occur?

There is more than one reason.

Firstly the simplest one is that the physical path from the negative terminal to the positive terminal does not have infinite resistance.
The resistance is very high, but over time, the minute current adds up to an appreciable loss of charge.

By physical  path I mean and include th air path, the path along the side of the (perhaps plastic) case and so on.

Secondly the chemical reaction within the battery is only the principle reaction.
Other competing reactions also occur, depending upon the type of battery.
Again in time their depleting effect is cumulative, reducing the reactants available for the wanted reaction.

Then the products of the reactions can occupy more space or otherwise leak (burst even) out of the case.
These products cause depositsof lower resistance which can partially or completely 'bridge' between the terminals.
Coin cells are particularly vulnerable to this issue.
You can often see the white semi crystalline deposits in the very narrow gap between the positive and negative terminals.
That is the time to I have just had to discard an LR44 from my kitchen scale for this reason. The voltage was reduced from 1.55V to 1.1V
Sorry it's gone to the battery recycling or I would post a photo.

Edited by studiot

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