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30 January, 13:05

At 400 K, the rate of decomposition of a gaseous compound initially at a pressure of 12.6 kPa, was 9.71 Pa s-1 when 10.0 per cent had reacted and 7.67 Pa s-1 when 20.0 percent had reacted. Determine the order of the reaction.

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  1. 30 January, 13:12
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    The order of the reaction with respect to the gas = 2

    Explanation:

    Let the original gas pressure be [G₀]

    Initial rate of reaction is given as

    r = k [G₀]ⁿ

    When 10% had reacted, amount of gas left = [0.9G₀], r = 9.71 Pa/s

    r = k [0.9G₀]ⁿ = 9.71 (eqn 1)

    when 20% had reacted, amount of gas left = [0.8G₀], r = 7.67 Pa/s

    r = k [0.8G₀]ⁿ = 7.67 (eqn 2)

    Dividing (eqn 1) by (eqn 2)

    (9.71/7.67) = [0.9/0.8]ⁿ

    1.266 = 1.125ⁿ

    1.125ⁿ = 1.266

    Take natural logarithms of both sides

    n (In 1.125) = In 1.266

    n = 0.236/0.118

    n = 2.
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