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Why do citric acid s clean pennies best




Q. My ten year old daughter and I read some of your letters about "What cleans pennies the best". She has 5 different juices: lemon, lime, pineapple, orange and grapefruit, she has actually found that lime has cleaned the best. However, with all of your letters, there is still not a research site or references given, so that she can back up her findings. She knows that the citric acid [on eBay or Amazon] is reacting with the copper, but why or how is this reacting in terms that she can understand and then write her report on. Thank you for any help.

Paticia H [last name deleted for privacy by Editor]
- Cleveland Heights, Ohio
2002


2002

A. We applaud her for actually doing the experiment instead of just asking for the answer, Patricia! It's also good that she is looking for high quality references, rather than the tossed salad of information, misinformation, and disinformation that is the internet. However, I do not personally agree with the structure & nature that you and perhaps the teacher seem to be trying to give to this investigation.

What is important for a ten year old student to get from a project of this nature (in my opinion) is the concept of "the scientific method" and the mechanics of a science project. She should be trying to learn the vocabulary: hypothesis, independent variable, dependent variable, control, lab book, observation, and conclusion. She should be learning that her efforts do not become a scientific experiment unless she follows a scientific protocol. She should be learning what "junk science" and "confirmation bias" are, why they are so poisonous, and how to avoid them. Please start with our FAQ on Cleaning Pennies as I think it will help.

The discoloration on old pennies is a copper oxide tarnish on them. Your daughter could also have "cleaned" the penny by applying sandpaper to it, scraping away that copper oxide tarnish and exposing the underlying copper metal. citric acid is an acid, and acids have the power to "clean" pennies, by dissolving this copper oxide tarnish. The tarnish dissolves into the acid and is washed away, exposing the "clean" non oxidized metal lying under it. Personally, I think that is enough depth for a ten year old. But the reaction is roughly:

Acid + copper oxide => copper salt + water

balancing the equation before proceeding:

2 acid + 1 copper oxide => 1 copper salt + 1 water

2 H+ [citrate anion]-- + Cu++ O-- --> Cu++[citrate anion]-- + H20

Acid has a 'sour' taste. So whichever fruit tastes the most sour may do the best job of cleaning. I agree with you that lime juice is quite good at removing tarnish from a penny. I'm not sure that it's better than lemon juice, though. It may depend on season, ripeness of individual piece of fruit, country where it was grown, etc. There is enough random variation in technique, tarnish depth, dirt on the pennies, etc., that the experiment may not have enough precision to resolve whether limes are better than lemons. But if repeated experiments demonstrate it, then we can perhaps assert it as true.

citric acid is not just an acid, but also a chelating agent. Even after college chemistry I don't fully understand chelation, and I doubt that you or the teacher do, and I don't believe that a 10 year old should be expected to. But it does aid in dissolving of the metal. There ought to be leads to references in the teacher's guide; or you might write to the publisher's website, since they should have the answer to the question they wrote.

Shake a few granules of salt into the lemon or lime juice and it will turn the penny salmon pink in a heartbeat. Why? Because the chloride from the salt is a very powerful copper corroder; but it is difficult to understand why this is so, too -- let alone explain it to a 10-year old.

I hope this reply may get you to slightly rethink what this experiment is supposed to be teaching your daughter. Not that I claim any special insight -- just that I have faced the questions from students hundreds of times on this site now now, and I think I'm starting to actually understand the issues :-)

Good luck!

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey



"Everything Kids Science"
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Q. Anion, Cation, Salt, Confusion...

I'm doing my 7th grade science project on what is the best way to clean a penny. For my research report to accompany it, I need to write about ions and salt and how it reacts with the copper/copper oxide. Please don't simplify... I may not be able to totally comprehend it but I guess I could ask my mom for help... Please respond ASAP! My teacher keeps telling me to explain more and more. I'm on my fourth draft. Please help me!
~sofia

Sofia F [last name deleted for privacy by Editor]
student - Berkeley, California
April 23, 2008


April 24, 2008

A. Hi, Sofia. As an aside, think about this: there are 3000-page books in the library that talk about ions; so how will you decide which pages of such books to leave out from your report? Easy: your research should be written in terms that explain or comment upon your own results. But you haven't told us your results! This may be the source of the confusion.

Try this:

"My hypothesis was . . . In order to try to prove that hypothesis, I conducted the following experiment . . . The results of my experiment tended to confirm my hypothesis but . . . I believe that the reason that this happened is because . . . This reasoning is supported by these excerpts from . . . which explain that . . ."

Ions are charged particles that are dissolved in a water-based solution. Positively charged ions are called cations, negatively charged ions are called anions.

Let's look at vinegar [in bulk on eBay or Amazon] for an example of cations and anions. vinegar is dilute acetic acid, and the formula for acetic acid can be written as HC2H3O2. vinegar will ionize as H+ + C2H3O2- , and the H+ are cations and the C2H3O2- are anions. As another example, citric acid from citrus fruits can be written as HCOOH, which will ionize as H+ + COOH- , where the H+ are cations and the COOH- are anions.

In either case the cations can react with copper to form copper salts as explained in the formulas in my previous response to Patricia. Good luck.

Regards,

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey



Q. Hi my name is Monica and I need help. I'm doing the same project and I was wondering does lemonade or Dr. Pepper clean the penny best? And why? Please answer ASAP.

Monica T [last name deleted for privacy by Editor]
student - Duluth, Georgia
November 13, 2008



A. Hi, Monica. It is your job to do the experiment. After you tell us which worked better, then we'll try to help you with why. Nobody can explain why you got the result you got until you tell us what result you got. And no one should try because that is called "junk science": deciding what the answer should be before doing the experiment, then talking yourself into discounting any contrary observations and giving far too much weight to observations which support the answer you want to get :-)

Good luck.

Regards,

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
November , 2008



Q. Hi my daughter is doing the cleaning the penny project. The 6 juices that she used was Apple, grape, grapefruit, lemon, cranberry, and orange. After reading on line the majority of the juices that cleaned the best was lemon. But, ours turned out to be that the cranberry juice in fact cleaned the best. Could you help us as to why ours is different?

Jodi Harris
student - millbrook, Alabama
January 20, 2010



A. Hi, Jodi. Maybe your cranberry juice was not pure juice, but a cranberry cocktail that had the tiniest smidgen of salt in it? Even "100% juice" cranberry juice isn't cranberry juice but "juice from apple, cranberry, pear and grape . . . citric acid . . . grape skins, pomegranate . . . ascorbic acid . . ."

It may be hopeless to try to explain why one juice manufactured to a secret formula cleans better than another juice manufactured to another secret formula, but you could try pH paper and see if it demonstrates anything :-)

Please see our FAQ on Cleaning Pennies and try to have your daughter learn how to conduct experiments and learn from them . . . and to not worry too much about whether the results agree with expectations. Good luck!

Regards,

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
January 20, 2010



Q. I'm a freshman and doing an project about which solution can "clean" a penny the best, and why. My results were that vinegar, salt and vinegar, ketchup, and lemon juice worked the best (over approx. a 10 hour time span). As far as I can tell, these all work in about the same way. (all acids. I've been researching why this is, but I've mostly been able to find only that acids dissolve the copper oxide. The only more "in depth" explanations I've found for both the role salt plays in this, and "how" the acids dissolve the copper oxide are TOO in depth, and written w/ the symbols that are past my understanding. Could you either give me, or direct me to somewhere I can get a "medium" explanation? I just need a simple "the copper bonds w/ the salt" or the acid breaks down into whatever and this can dissolve the copper oxide. I'm not even sure that you (or anyone) can give me this type of an explanation, but I'm at least trying! Thanks, you're site has already been really helpful!

Christian G [last name deleted for privacy by Editor]
- College Park, Maryland
April 5, 2010



April 6, 2010

A. Hi, Christian. Two common acids are
HCl, which is muriatic (hydrochloric) acid, used for dissolving mortar & grout, and pickling metal, and
H2SO4, which is sulfuric acid, used in car batteries and a host of other applications.

If you note what they have in common, they start with H for hydrogen. In water, HCl will dissolve or ionize into the charged ions H+ and Cl-; and sulfuric acid will ionize into H+, H+, and SO4-2

Most other acids are written in rather similar form:
H3PO4, phosphoric acid
HNO3, nitric acid
HC2H3O2, acetic acid or vinegar
H3C6H5O7, citric acid

We measure acidity on the pH scale, which tells us how much H+ has ionized into the solution. Basically, the lower the pH, the more acidic the solution is, and the more capable of attacking metals, rusts, and oxide tarnishes.

A penny, whether it is an old solid copper penny or a newer zinc-core penny, has a skin of copper. The copper metal (Cu) has reacted with oxygen in the air (O) to form copper oxide tarnishes like Cu2O. When you remove the tarnish from a penny with an acid, the chemical reaction is something like:

2HCl + Cu2O => H2O + 2CuCl, with the copper oxide now dissolved and the "clean" copper metal exposed again.

Basically, the stronger the acid, the faster and better it will work.

Salt is sodium chloride, NaCl. It is difficult to explain why salt helps as much as it does, except to say that chloride salts like CuCl are very soluble in solution, so the reaction tends to easily proceed, without much impediment or backsliding (chemical reactions don't actually proceed entirely in one direction: there tends to be an equilibrium reaction, with the reaction trying to proceed in the "other" direction to some extent). Perhaps if you quickly get the generated copper "out of play" by tying it up as highly soluble CuCl, the reaction proceeds faster?

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey


thumbs up signThank you so much for your help! Hope I didn't "bombard" you with the same question again, it was just one I still had left over after reading the FAQ. Thanks a bunch!

Christian G [last name deleted for privacy by Editor]
- College Park, Maryland
April 6, 2010




Q. I need some dash notes on which juices clean pennies better.

kerry_lynn_c
Kerry Lynn C
- Cowpens, South Carolina, USA
December 5, 2014


A. Hi Kerry. Please see the previously mentioned "FAQ on Cleaning Pennies".

You call them "dash notes" and I guess that's best in school these days. We used to call them bullets :-)

Best of luck.

Regards,

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
December 2014



April 24, 2015

A. Hi there. I thought I would attempt to add some ideas for those doing high school level science fair projects involving the cleaning of pennies or other copper objects by use of weak organic acids with or without adding chloride salts.

First I want to note that I'm still in college (working towards a major in materials science), so I am by no means an expert on the subject. That said, I feel I have some helpful ideas for those conducting this type of experiment.

As Ted has pointed out, chloride salts such as NaCl may aid the dissolution of copper(II) oxide CuO by the high solubility of copper chloride CuCl2 over say copper(II) citrate Cu3(C6H5O7)2 (which is a much more complex structure). I should note that the effects of spectator ions (like Cl- or citrate) in solution is complicated and beyond the scope of the primary experiment.

We now know that the presence of chloride ions can affect the efficacy of the cleaning process. Consequently, we can't be sure if one cleaning solution is really better than another since we don't know if chloride ions are present in any of the test solutions. As a result, we need to test each cleaning solution for its presence. This can be done qualitatively by adding a few drops of silver nitrate AgNO3 solution to a small sample of each cleaning solution. If chloride ions are present silver chloride AgCl(s) precipitate will form and you will see a milky white suspension that will slowly settle.

AgNO3(aq) + NaCl(aq) --> AgCl(s) + NaNO3(aq)

Next you will want to measure the pH of each test solution to determine the concentration of H+. This can be done semi-quantitatively using pH test strips--paper that changes color based upon the strength of the H+ concentration of the solution. The lower the pH the higher the H+ concentration and consequently the faster the reaction will take place when the penny is added to the solution.

Since we are now talking about acids, its importation to know that fruits and vegetables contain many different types of weak organic acids. An important quantity to know for weak acids is the acid dissociation constant K_a which lets you know to what extent the acid will ionize or give off H+ when dissolved in water?basically, most of the acid in solution will remain inactive (or unionized).

Citric acid: C6H8O7, found in many types of fruit, is triprotic and can release up to 3H+ when dissolved into water. Being a weak acid however, you won't lose all three H+ unless you have a strong base present. It?s acid dissociation constants are K_a1 = 7.4e-4, K_a2 = 1.7e-5 and Ka_3 = 4.0e-7.

Ascorbic acid: C6H8O6, found in lemons and limes, is diprotic and can release up to 2H+ when dissolved into water. It?s acid dissociation constants are K_a1 = 8.0e-5 and K_a2 = 1.6e-12.

Malic acid: C4H6O5, found in green apples, and is also diprotic. It?s acid dissociation constants are K_a1 = 4.0e-4 and K_a2 = 7.7e-6.

Oxalic Acid: C2H2O4, found in rhubarb (a leafy red/green vegetable) and beets, is diprotic. It?s acid dissociation constants are K_a1 = 5.9e-2 and K_a2 = 6.4e-5.

Acetic acid: C2H4O2, found in vinegar, is monoprotic and releases one H+ when dissolved into water. It's acid dissociation constant is K_a = 1.8e-5

As far as the first K_a value goes, oxalic acid is the strongest, with citric acid and malic acid following in second and third respectively. What this all boils down to, is if you had solution of each acid all at the same concentration, the one with the highest K_a value would clean the penny the fastest. Which means it is important to time how long you submerge your penny and repeat that same process for each test solution. This also gives a more scientific indication as to which solution you would predict to be the better cleaning solution.

Bringing the last two ideas together, measuring the pH and identifying which acid is in the test solution, it's good to know that the connection between the pH of a weak acid solution and the concentration of that acid in solution is a bit tricky. For weak acids, the more concentrated the solution the less the acid ionizes. So while pH does decrease for more concentrated solutions, it decreases more slowly as the concentration goes up. This implies that a super concentrated solution isn't terribly more effective at cleaning the penny as a more dilute one. It also implies that solutions of two different acids at two different concentrations can give similar pHs. However, the speed at which one solution cleans over the other will dependent mostly on the K_a value for that acid. In conclusion, knowing the pH isn't enough information to decide if that solution will clean better (faster).

It could be a good idea to dilute the test solutions to the same pH, that way your results are mostly affected by the value of K_a of the specific acid/s in that solution. This would allow you to make a more definite prediction as to which solution will be the most effective. Basically you would measure the pH of each solution, find the one with the highest pH and dilute the others until the indicator paper gives the same color as that solution.

If you choose to not equalize the test solution's pH, it's also important to note that a lower pH solution may not achieve as good of results in comparison to a weaker solution which contains chloride ions. This effect may actually make a better science fair project: Do spectator ions influence the rate of reaction (act as a catalyst)? You could use an iodide salt like potassium iodide KI and a sulphate salt like magnesium sulphate MgSO4 to test against a control having no salt and the chloride salt to see if only chloride ions exhibit the effect.

Whew! That's a lot to take in. Maybe we should do a small cliff note summary: Spectator ions can affect the rate of reaction, solution pH affects the rate of reaction, K_a of the dominate acid will affect the rate of reaction (most noticeably if each solution has the same pH). Focusing on the effects of K_a or different types of spectator ions as potential catalysts would likely make your project seem more noteworthy and well thought out.

The reaction taking place during cleaning depends upon which acid/s you have in solution. Using acetic acid as an example we get:

CuO(s) + 2 CH3COOH(aq) --> H2O(l) + Cu(CH3COO)2(aq)
CuO(s) + 2 H+(aq) --> H2O(l) Cu(2+)(aq)

If NaCl(aq) is present it remains as spectator ions and is not included in the reaction. However, the presence of aqueous chloride ion Cl-(aq) may act as a catalyst, if so; you can write the equation as:

CuO(s) + 2 Cl-(aq) + 2 CH3COOH(aq) --> H2O + Cu(CH3COO)2(aq) + 2 Cl-(aq)

It's good to know that by cleaning the penny with the process you are removing a small amount of copper from the penny. So if you were to carefully weigh it before and after the acid dip you would see a small change in mass, dependent upon how much oxidized copper was present.

For fun, you can test your solution for copper 2+ ions by placing a metal more active than copper, like zinc or iron, into the solution and look to see if any copper is reduced (plated) onto its surface. You may want to neutralize the solution with some baking soda first so that the active metal doesn't react with H+ from the acidic solution to form H2(g) and a salt of that metal.

G. Raymond Mackenzie
- Cedar City, Utah , USA




Experimental Variable and Controlled Variables?

13443

Q. How can we determine the Experimental Variable and the Controlled Variable for my son's 5th grade science fair project? We have done the experiment for cleaning coins and came across your information on www.finishing.com/faqs/pennies.shtml and various letters here that are very helpful. I'm having a hard time assisting my son with this part of the packet and I wondered if you could help by showing examples so I can figure out what these answers are for his project? Thanks for all the valuable information on this site!

Lori Huntsman
Parent of 5th grader - Riverton, Utah USA
January 26, 2016



A. Hi Lori. This is going to be "ducking the question" a bit, but the FAQ you referenced already explained my understanding of independent variables and dependent variables ...

... and I don't want to assert for sure that "experimental variable" has exactly the same connotations as "independent variable" and that "controlled variable" has identical connotations to "dependent variable". But I think that they are much the same thing, i.e., that an independent or experimental variable is something which you choose to vary (like the temperature, the immersion time, the dilution of your treatment chemical ... or in your case, what chemical you use) and a dependent variable or controlled variable is what changes as a result (how much tarnish gets removed, how much weight is lost, how bright the pennies become).

A point that I repeatedly make (probably to the point of ennui for our regular readers) is that it's fine for a student to ask for help with an answer, but it's no good to ask for help understanding the question or the assignment; that has to be clarified with the teacher :-)

Regards,

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
January 2016




Q. Hi, my daughter has an experiment on, What is the effect of different liquids on pennies? She used: water, vinegar, Coca-Cola, bleach, Redbull, rubbing alcohol, and Mt Dew. She is leaving them in the liquids for one week. She has been making observed actions every day.

The bleach seems to be eating through the penny and the others seem to not be changing the pennies much. After doing some research we realized we should have used pennies all from before 1983 and maybe used salt in with the vinegar. She has 5 days left before her project is due. Should we restart the project and change some of the variables, or maybe not do not for such a long period. Please help! Thank you.

Shannon Hendrickson
- Santa Teresa New Mexico, US
February 17, 2016


A. Hi Shannon. Personally, I think understanding the ideas and the procedures is more important than interpreting the results, so I would keep on going. She now realizes that mixing pennies from pre and post 1983 introduces a variable, and she understands why; so now it's a matter of explaining what her research found on the subject. She has learned that salt added to the vinegar probably would have speeded up the corrosion, and those two research findings are nice for a discussion of "next time".

If she has access to pH paper, it would be nice to know the pH's so she has a sound variable she can chart; if the results do not track the pH, that's fine. Half of her reagents have secret ingredients, so absolute cause-and-effect will elude everyone. Drawing some inferences despite inconclusive results, and planning how to hopefully do better next time, is how science, technology, learning, and life works. Best of luck to her.

Regards,

Ted Mooney, finishing.com
Ted Mooney, P.E.
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
February 2016




Q. Hi Ted,

My name is Rachel and I am an 8th grader attending the Special Music School in Manhattan. I am currently working on my Science Exit Project experiment, which is cleaning oxidized pennies using a combination of acids and bases. I used vinegar, lemon juice, milk and soapy water in my experiment. After doing the experiment once, (and my teacher told me I have to do at least 10 more trials to be sure) I found out that vinegar cleaned the oxidized pennies the best. However, I was a bit surprised because I was wondering, "What about the lemon juice? Shouldn't it have cleaned the pennies the best too, since it was also an acid?" Could you please explain to me why this is so? That would be greatly appreciated. I'm am looking forward to your answer!

Rachel J [last name deleted for privacy by Editor]
- New York City, United Sates, New York
April 29, 2016


A. Hi Rachel. Your teacher has given you outstanding advice, but I think you are only partially understanding it.

Her point seems to be that one test isn't enough for you to be confident of your result (some miscellaneous/random/fluke condition might have been involved in that single test which corrupted the results). She wants you to repeat it ten times so you have some real confidence that there is in fact a scientific reason for the result. But you are asking for the scientific reason for the result you got before you have sufficient evidence to assume that there is one :-)

If you do it the teacher's way you are practicing the scientific method. If you do it the other way you risk getting involved in "junk science" and "confirmation bias"; let me explain why --

You think, based on a single test, that there's a scientific reason that vinegar is better than lemon juice. Now suppose I do what you ask and tell you there is, and I explain it to you with impressive fancy looking formulas that you only half understand. Then you start the first confirmation trial, and you get a different result. Now you're sure this must be an error because it contradicts both your experience and the fancy explanations; you now have a bias and you'll be telling yourself: I know vinegar is better, and this web page confirmed it, and explained it, so I must have done something wrong this time. And you will put too much weight on any results that go along with the bias, discount any results that don't, and generally be fudging your findings to agree with that bias. So do the 10 tests, and only THEN look for the reason :-)

Regards,

pic of Ted Mooney
Ted Mooney, P.E. RET
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
April 2016


A. Rachel,
Keep in mind that "also an acid" can mean a wide variety of things.

Sometimes any old acid will do the job. Sometimes certain acids will do the job a lot better than other acids will. Concentration is also a factor. Even the same acid might not do the same job if the amount of acid is lower. Also consider the mix may not be a pure acid. In manufacturing we sometimes add other things to the acid to help it along, but if you add the wrong thing it might make it work less well.

One of the things you can do in your report is propose a follow up experiment (not actually do it, just talk about it) in which you remove the things that are different between your two samples. Instead of lemon juice and vinegar, use the pure version of the two acids in those materials and mix them up in identical concentrations. Then it would be a fair comparison.

ray kremer
Ray Kremer
Stellar Solutions, Inc.
supporting advertiser
McHenry, Illinois
stellar solutions banner
May 2, 2016


thumbs up signThanks both of you for helping me out!😄😀

Rachel Joo [returning]
- New York City, United States, New York
May 3, 2016


A. After reading this stuff, I feel compelled to give a more COMPLETE answer about the 'pennies, vinegar, and, salt' experiment. I find it a bit difficult to believe that college educated CHEMISTS either don't know this, or think it unnecessary to include in the 'explanation'. Here goes in as simple terms as possible: When vinegar (dilute acetic acid) and salt (sodium chloride) are mixed together, a process called 'HYDROLYSIS' occurs where the 'CHLORIDE' in the SALT is HYDROLYZED by the weak acid in the vinegar to form a very weak solution of 'HCl' (hydrogen chloride). This (HCl) is otherwise known as 'HYDROCHLORIC', or, 'muriatic' acid, and it is THIS that dissolves the brown patina, or, "copper oxide" from a penny making it look 'CLEAN'. vinegar is not a strong enough acid to easily remove these "oxides" (and 'carbonates') from 'tarnished' copper (or, brass, bronze, etc). Hope this wasn't TOO complicated, and I hope it finally addresses what really happens for those who might be interested.

Richard Mathis
- Birmingham, Alabama, U.S.A
August 17, 2016



My tongue hurts from biting it.
Regards,

pic of Ted Mooney
Ted Mooney, P.E. RET
Striving to live Aloha
finishing.com - Pine Beach, New Jersey




Q. What is your opinion on cleaning pennies and why? How does it benefit you and your daily life? Please answer ASAP!

Jazlyn Wood
- Riverside, California, United States
January 6, 2017


A. Hi Jazlyn. I don't think it does benefit me; I prefer tarnished pennies. How about you?

Regards,

pic of Ted Mooney
Ted Mooney, P.E. RET
Striving to live Aloha
finishing.com - Pine Beach, New Jersey
January 2017




Q. Hello, I'm currently trying to think through my 9th grade science fair project, and I was going to soak several pennies in several different liquids. My only problem is, you see, I don't know how to make sure all my pennies are the same, as in, how will I know that they are all the same in what has made them dirty? Do you have any ideas in how to fix this? Or do you think it won't really matter? Thanks in advance ;)

rosea angelo
- boise, idaho, united states of america
October 18, 2017


A. Hi Rosea. Congratulations on making the effort to think it through -- that's very important. There is probably not any good way for you to know for sure that two pennies are broen for exactly the same reason, just as there is no way to say for sure that if you tossed those coins they would not turn up heads 12 times in a row. Rather, you need to think in probables, which is one reason experiments are repeated.

So if you have a pile of pennies and you take 6 for each group in your test, the odds are awfully small that all 6 in one group are brown for the same one reason, but the 6 in the next group are all brown for a different reason than the pennies in the first group. Good luck.

Regards,

pic of Ted Mooney
Ted Mooney, P.E. RET
Striving to live Aloha
finishing.com - Pine Beach, New Jersey




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