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Quantized Charge Problem, Why is this right?

  1. Jul 23, 2007 #1
    1. The problem statement, all variables and given/known data

    26. Calculate the number of coulombs of positive charge in 250 [itex]cm^3[/itex] of (neutral) water. (Hint: A hydrogen atom contains one proton; an oxygen atom contains eight protons.)

    2. Relevant equations

    [tex]
    q = n_{e}e, n_{e} = \pm1, \pm 2, \pm 3,...,
    [/tex]

    e [itex]\equiv[/itex] elementary charge

    [tex]
    e = 1.60217646{\textcolor[rgb]{1.00,1.00,1.00}{.}}x{\textcolor[rgb]{1.00,1.00,1.00}{.}}10^{-19}
    [/tex]

    3. The attempt at a solution

    [tex]
    q = n_{e}e, n_{e} = \pm1, \pm 2, \pm 3,...,
    [/tex]

    [itex]n_{p} \equiv[/itex] number of protons
    [itex]q_{p} \equiv[/itex] charge on a single proton

    [tex]
    q_{p} = +e
    [/tex]

    [tex]
    q = \left(n_{p}\right)\left(q_{p}\right)
    [/tex]

    Z [itex]\equiv[/itex] Atomic Number (Number of Protons)
    m [itex]\equiv[/itex] mass
    M [itex]\equiv[/itex] Molar Mass ([kg]/[mols])

    [tex]
    \rho_{w} = \frac{m_{w}}{V_{w}}
    [/tex]

    [tex]
    n_{p} = \frac{m_{w}}{m_{H_{2}O}} \cdot \frac{Z_{H_{2}O }}{1}
    [/tex]

    [tex]
    n_{p} = \frac{m_{w}}{\left(2m_{H}+1m_{O}\right)}} \cdot \frac{\left(2Z_{H}+1Z_{O}\right)}{1}
    [/tex]

    [tex]
    q = \left(\frac{\left(V_{w}\rho_{w}\right)}{2m_{H}+1m_{O}} \cdot \frac{2Z_{H}+1Z_{O}}{1}\right)q_{p}
    [/tex]

    [tex]
    q = \left(\frac{V_{w}\rho_{w}}{2\left(\frac{M_{H}}{N_{A}}\right)+1\left(\frac{M_{O}}{N_{A}}\right)} \cdot \frac{2Z_{H}+1Z_{O}}{1}\right)q_{p}
    [/tex]

    [tex]
    q = \left(\frac{N_{A}V_{w}\rho_{w}}{2M_{H}+1M_{O}} \cdot \frac{2Z_{H}+1Z_{O}}{1}\right)q_{p}
    [/tex]

    The above equation yields the correct solution, however my question is why is this right as opposed to the following?

    [tex]
    q = \left(\frac{m_{w}}{m_{p}}\right)q_{p}
    [/tex]

    [tex]
    q = \left(\frac{V_{w}\rho_{w}}{m_{p}}\right)q_{p}
    [/tex]

    Why is the previous equation wrong?

    Any help is appreciated.

    Thanks,

    -PFStudent
     
    Last edited: Jul 24, 2007
  2. jcsd
  3. Jul 23, 2007 #2

    Kurdt

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The last equation assumes that the mass of the water is made entirely from protons which of course is not true.
     
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