1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Percent copper in post-1982 pennies

  1. Sep 9, 2013 #1
    % copper in post-1982 pennies

    1. The problem statement, all variables and given/known data
    The total mass of each penny is 2.500g, the density of copper is 8.96g/ml, the density of zinc is 7.14g/ml and the mass of a penny if it was 100% copper would be 3.11g.


    2. Relevant equations



    3. The attempt at a solution
    I am not too sure how to start this one. If someone could give me a boost I would appreciate it.
     
  2. jcsd
  3. Sep 9, 2013 #2
    Sorry not the clearest. I want to know the percent composition by mass of zinc and copper.
     
  4. Sep 9, 2013 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You can figure the volume of the penny by using the figures for 100% copper. Once you do that, you can write an algebraic equation for the penny which is composed of a mixture of copper and zinc.
     
  5. Sep 10, 2013 #4
    Ok well I got the volume of a penny to be 0.347ml. The only equation I can think to set up is

    0.347ml=x(1ml/8.96)+y(1ml/7.14) From this I need a way to solve for x or y.?.?
     
  6. Sep 10, 2013 #5

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You don't necessarily want to calculate the volume of the penny; that has already been done. You want to find out what the percentage of copper and zinc are in the new penny which has a mass of 2.500 g.

    Whatever part of the new penny which isn't copper must be zinc. So, if x is the percentage of copper, what must the percentage of zinc be in the new penny?
     
  7. Sep 10, 2013 #6

    Borek

    User Avatar

    Staff: Mentor

    There is another equation. x and y are fractions of zinc and copper - what is their sum?

    SteamKing points you in the same direction, he just tries to use a single variable.
     
  8. Sep 10, 2013 #7
    Well the answer I'm getting can't be right because it is more than 100%. The equations I set up though are

    x+y=2.500g ==> x=2.500g-y

    0.357ml=(2.500g-y)(1ml/8.96)+y(1ml/7.14)

    x represents copper and y represents zinc.
     
  9. Sep 10, 2013 #8

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    That's because you're not paying attention. If x = percentage of copper, what must be the percentage of zinc in the new penny?
     
  10. Sep 10, 2013 #9
    The percentage of zinc would be (100-x). So I should eliminate the variable y and replace it with (100-x). So my equation would be 0.357ml=(x)(1ml/8.96)+(100-x)(1ml/7.14) Right?
     
  11. Sep 10, 2013 #10

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    That's not right. You might find it easier to work with x as a fractional part (a number between 0 and 1) rather than a percentage. It's trivial to convert that fractional part to a percentage.
     
  12. Sep 10, 2013 #11
    So your saying that I should use (1-x) instead of (100-x)? making my equation
    0.375ml=(x)(1ml/8.96)+(1-x)(1ml/7.14)
     
  13. Sep 10, 2013 #12
    This equation still does not work. I get a negative number and something greater than 100%. What am I doing wrong?
     
  14. Sep 10, 2013 #13

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Don't drop units! If you had kept the units intact you would have seen that this is the wrong equation. That 8.96 and 7.14: Those are densities. Both terms on the right hand side have units of volume/density, or volume2/mass. The left hand side has units of volume. Your equation has inconsistent units.

    Hint: You haven't used the fact that the penny's mass is 2.5 grams.
     
  15. Sep 10, 2013 #14

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Been trying to tell OP that since Post #5.
     
  16. Sep 10, 2013 #15
    The reason my units are just ml on the right hand side is because (x gCu)*(1ml/8.96 gCu) =x(1ml/8.96). The same is true for the other expression.
     
  17. Sep 10, 2013 #16

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    x has to be unitless.
     
  18. Sep 10, 2013 #17
    Well how do I get x unitless? I felt bad about not getting this problem but when I got to class turned out no one else I could find got it either. Are my equations even close to correct?
     
  19. Sep 11, 2013 #18

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    No. We've been trying to tell you that, but you haven't taken heed of our suggestions.

    Forget the volume of the penny. That has already been calculated. It is the same for both the old penny and the new penny.

    What you must find out is how much copper and how much zinc it takes to make a penny which has a mass of 2.500 grams.

    You can use the mass of the new penny to figure out what the average density of the penny must be, given its mass of 2.500 grams. You also are given the densities of copper and zinc.

    Once you know the average density of the new penny, you can write an algebraic equation using the densities of Cu and Zn to find out the proportions of the mixture which gives this average density.
     
  20. Sep 11, 2013 #19
    What you must find out is how much copper and how much zinc it takes to make a penny which has a mass of 2.500 grams.
    You can use the mass of the new penny to figure out what the average density of the penny must be, given its mass of 2.500 grams. You also are given the densities of copper and zinc.

    I calculated the average density to be 2.80g/ml.

    Once you know the average density of the new penny, you can write an algebraic equation using the densities of Cu and Zn to find out the proportions of the mixture which gives this average density.

    An average density can be useful? That will not yield an inaccurate calculation?
     
    Last edited: Sep 11, 2013
  21. Sep 11, 2013 #20
    1234 ignore this
     
    Last edited: Sep 11, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Percent copper in post-1982 pennies
  1. Percent Yield (Replies: 4)

  2. Percent Abundance (Replies: 2)

  3. Percent Yield (Replies: 7)

  4. Percent Composition (Replies: 1)

Loading...