Consider this reaction: At a certain temperature it obeys this rate law. rate Suppose a vessel contains at a concentration of . Calculate how long it takes for the concentration of to decrease by . You may assume no other reaction is important. Round your answer to significant digits.

This question is incomplete, the complete question is;

Consider this reaction:

2H₃PO₄(aq) → p₂o₅(aq) + 3H₂O(aq)

At a certain temperature it obeys this rate law.

rate = ( 46.65 M⁻¹.s⁻¹) [ H₃PO₄ ]²

Suppose a vessel contains H₃PO₄  at a concentration of 0.660 M .

Calculate how long it takes for the concentration of H₃PO₄  to decrease  to 20.0% of its initial value .

You may assume no other reaction is important.

Round your answer to significant digits.

time taken is 8.574 × 10⁻⁴ s

Explanation:

Given that;

rate = k[ H₃PO₄ ]²

rate constant k = 46.65 M⁻¹.s⁻¹)

Initial concentration A₀ =  0.660 M { which will be 100%}

final concentration At = 20%

for the concentration of H₃PO₄  to decrease  to 20.0% of its initial value = ?

we know that;

rate constant k =  1/t [ 1/At - 1/A₀ ]

we substitute

46.65 = 1/t [ 1/20 - 1/100 ]

46.65 = 1/t [ 0.04 ]

46.65 = 0.04/t

46.65t = 0.04

t = 0.04 / 46.65

t = 0.0008574  ≈ 8.574 × 10⁻⁴ s

Therefore, time taken is 8.574 × 10⁻⁴ s

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