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Word problem to understand the large size of Avogadro's Number

  1. Dec 6, 2015 #1

    E20

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    1. Asume that you distribute Avogadro's Number of dollars evenly among each of the 4.5 x 109 people on earth. Further, assume that everyone spends $1000 each second, day and night.
    What percentage of each person's wealth will have been spent after one year?
    2. Avogadro's Number = 6.02 x 1023


    3. a) "distribute evenly among" = (6.02 x 1023 / 4.5 x 109)
    because $/ppl

    b) "everyone spends $1000 each second... after one year" = ($1000 x 3.1536 x 107 s) = 3.1536 x 1010
    (31536000 = 60 s x 60 min x 24 hr x 365 day)

    c) "What percentage of each person's wealth will have been spent after 1 year"
    each person's total wealth = x
    percent spent = n
    $/year = 3.1536 x 1010

    percent spent / each person's total wealth = total spent / amount distributed


    n / x = (3.1536 x 1010 s) / (6.02 x 1023 / 4.5 x 109)

    cross multiplying leaves me with:

    (6.02 x 1023)n = (3.1536 x 1010 x 4.5 x 109)x

    ----
    This is an exercise in my chem book, trying to get us to appreciate the scale of Avogadro's Number.. so it isn't answered. But, is this the correct way to think a problem like this through?
    @_@
     
  2. jcsd
  3. Dec 6, 2015 #2

    DrClaude

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    Staff: Mentor

    This is not correct. If your total wealth was $10000 and you spent 20% of that, what would the equation look like?
     
  4. Dec 6, 2015 #3

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Boy, is this problem old! The world's population was estimated to be 4 billion in 1974 and 5 billion in 1987. It hasn't been 4.5 billion in about 30 years or so.
     
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