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For a first-order reaction, Tₓ% denotes the time required to complete x% of the reaction. Given T₇₅% = A * T₅₀%, T₈₇.5% = B * T₅₀%, and T₉₉% = C * T₉₀%, find A + B + C.
- 7
- 14
- 21
- 5
Correct answer: 7
Solution
For first order: t = (1/k) * ln(100/(100-x%)). T₅₀% = ln2/k, T₇₅% = ln4/k, T₈₇.5% = ln8/k, T₉₀% = ln10/k, T₉₉% = ln100/k. A = T₇₅%/T₅₀% = ln4/ln2 = 2. B = T₈₇.5%/T₅₀% = ln8/ln2 = 3. C = T₉₉%/T₉₀% = ln100/ln10 = 2. A + B + C = 2 + 3 + 2 = 7.
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