Question #191956

A first order reaction is 30 percent completed in 35 minute what is the value of the rate constant?

b) whay percent of the reactant will remain after 5 hours?

Expert's answer

**Solution:**

Let 1 M - the initial concentration, [A]_{o}.

After 35 minutes, the concentration, [A], is: 1 - 0.3 = 0.7 (M)

a)

For a first order reaction**:**

ln[A] = −kt + ln[A]_{o}

Hence,

ln(0.7) = −k × 35 + ln(1)

ln(0.7) = −k × 35

-0.3567 = −k × 35

**k = 0.01019 min**^{-1}

b)

(5 h) × (60 min / 1 h) = 300 min

ln[A] = −kt + ln[A]_{o}

ln[A] = (−0.01019 × 300) + ln(1)

ln[A] = -3.057

[A] = e^{-3.057} = 0.047

0.047 M × 100% / 1 M = 4.7%

So, **4.7%** of the reactant will remain after 5 hours.

**Answers:**

**a) The value of the rate constant (k) is 0.01019 min**^{-1}

**b) 4.7% of the reactant will remain after 5 hours**

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