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For a first-order reaction with an initial concentration of 2.00 M, a time duration of 200 minutes, and a final concentration of 0.15 M, the rate constant (k) is calculated using which expression?
- k = 2.303/t log (a/(a-x))
- k = 2.303 log (a/(a-x))
- k = 2.303/t log (2.00/0.15)
- k = 2.303 log (2.00/0.15)
Correct answer: k = 2.303/t log (2.00/0.15)
Solution
The formula for the rate constant of a first-order reaction is k = (2.303/t) log (a/(a-x)). Substituting the given values (a = 2.00 M, a-x = 0.15 M, t = 200 min), the correct expression is k = 2.303/t log 2.00/0.15.
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