### Chemical Kinetics: Reaction Rate ProblemConsider the following reaction:\[ 2H_3PO_4(aq) \rightarrow P_2O_5(aq) + 3H_2O(aq) \]At a certain temperature, it follows this rate law:\[ \text{rate} = (0.048 \, \text{M}^{-1} \cdot \text{s}^{-1}) [H_3PO_4]^2 \]#### Problem Statement:Suppose a vessel contains \( H_3PO_4 \) at an initial concentration of \( 1.06 \, \text{M} \). Calculate the time required for the concentration of \( H_3PO_4 \) to decrease to \( 0.053 \, \text{M} \), assuming no other reactions are significant.Please round your answer to two significant digits.#### Input Box:- **Answer box placeholder:** _s (seconds)---#### Explanation of Calculation:To solve for the required time (\( t \)), we need to integrate the rate law for a second-order reaction, which is in the form:\[ \frac{1}{[A]_t} = \frac{1}{[A]_0} + kt \]where:- \([A]_t\) is the concentration of \( H_3PO_4 \) at time \( t \)- \([A]_0\) is the initial concentration of \( H_3PO_4 \)- \( k \) is the rate constant- \( t \) is timeGiven data:- \([H_3PO_4]_0 = 1.06 \, \text{M}\)- \([H_3PO_4]_t = 0.053 \, \text{M}\)- \( k = 0.048 \, \text{M}^{-1} \cdot \text{s}^{-1} \)By substituting the given concentrations and rate constant into the integrated rate law, we can solve for \( t \).

Answered: Image /qna-images/answer/73787c2c-5fbc-4c62-a09c-720783badb09.jpg

Consider this reaction: 2H₂PO4 (aq) → P₂O, (aq) + 3H₂O (aq) - At a certain temperature it obeys this rate law. rate = (0.048 M¹.s¹) [H₂PO₂] S Suppose a vessel contains H₂PO at a concentration of 1.06 M. Calculate how long it takes for the concentration of H₂PO to decrease to 0.053 M. You may assume no other reaction is important. Round your answer to 2 significant digits. ☐x10

Consider this reaction: 2H₂PO4 (aq) → P₂O, (aq) + 3H₂O (aq) - At a certain temperature it obeys this rate law. rate = (0.048 M¹.s¹) [H₂PO₂] S Suppose a vessel contains H₂PO at a concentration of 1.06 M. Calculate how long it takes for the concentration of H₂PO to decrease to 0.053 M. You may assume no other reaction is important. Round your answer to 2 significant digits. ☐x10

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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