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Math Help - Rate of Reaction

  1. #1
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    Rate of Reaction

    Experiments show that if the chemical reaction
    N2O5 --> 2NO2 + 1/2 O2
    takes place at 45 C, the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows:
    -d[N2O5]/dt=0.0002[N2O5]
    How long will the reaction take to reduce the concentration of [N2O5] to 90% of its original value?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by asnxbbyx113 View Post
    Experiments show that if the chemical reaction
    N2O5 --> 2NO2 + 1/2 O2
    takes place at 45 C, the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows:
    -d[N2O5]/dt=0.0002[N2O5]
    How long will the reaction take to reduce the concentration of [N2O5] to 90% of its original value?
    ok. whenever i see chemistry, my brain freezes up, so don't take this answer too seriously.

    - \frac {d [N_2 O_5]}{dt} = 0.0002[N_2 O_5]

    \Rightarrow \frac {d [N_2 O_5]}{dt} = - 0.0002[N_2 O_5]

    \Rightarrow \frac {1}{[N_2 O_5]} \frac {d[N_2 O_5]}{dt} = -0.0002

    \Rightarrow \ln [N_2 O_5] = -0.0002t + C

    \Rightarrow [N_2 O_5] = Ae^{-0.0002t}

    A is the initial concentration of N_2 O_5. We want the time when we have 90% of this concentration.

    So, we want:

    0.9A = Ae^{-0.0002t}

    \Rightarrow 0.9 = e^{-0.0002t}

    Now we solve for t and that should be your answer
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