**Transcription for Educational Website:**---**Chemical Kinetics and Equilibrium Problem Set**1. **Decay of Isotope Z:** - The half-life of isotope Z is 4.0 years. If the reaction is first order, how many years would it take for an 8.00 mg sample of isotope Z to decay and have only 1.00 mg remaining? Answer in years: ____2. **Equilibrium Constant for Ammonia Formation:** - Reaction: \( N_2(g) + 3 \, H_2(g) \rightarrow 2 \, NH_3(g) \) - The value of \( K_p \) at 25 degrees Celsius for this reaction is \( 4.5 \times 10^{-12} \). - Determine the value of \( K_c \): ____ - *Note: No units are necessary.*3. **Universal Gas Constant:** - \( R = 0.08206 \, \text{Latm/molK} \)4. **Equilibrium Constant from Gibbs Free Energy:** - For the reaction \( Fe_3O_4(s) + 4 \, CO(g) \rightleftharpoons 3 \, Fe(s) + 4 \, CO_2(g) \) - Given \( \Delta G^\circ = -12.3 \, \text{kJ} \) at 298 Kelvin, calculate the \( K_{eq} \). - Answer to the nearest whole number: ____---**Note:** This set of problems is designed to explore concepts of chemical kinetics and equilibrium, including the application of first-order decay laws and the interplay between \( \Delta G^\circ \), \( K_p \), and \( K_c \) in chemical reactions.

Since you have posted multiple questions, we will provide the solution only to the first question as per our Q&A guidelines. Please repost the remaining questions separately.Q.1 Given: Half-life of isotope Z = 4.0 years Initial amount of Z = 8.00 mg Left amount of Z = 1.00 mg Order of the reaction = 1The decay constant is related to the half-life by the following relation: λ=0.693t1/2 ......(1) Substitute the known values in equation (1). λ=0.6934.0 yr=0.173 yr-1The integrated rate equation for first order reaction is: Nt=Noe-λt ......(2) Here, No is the initial amount and Nt is the remaining amount of isotope after time t. Substitute the known values in equation (2). 1.00 mg=8.00 mg×e-0.173×te-0.173×t=1.00 mg8.00 mge-0.173×t=0.125-0.173×t=ln0.125t=-2.08-0.173 yr=12 yr Hence, the decay time is 12 years.

Answered: The half-life of isotope Z is 4.0…

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Chemistry

The half-life of isotope Z is 4.0 years. If the reaction is first order, how many years would it take for an 8.00 mg sample of isotope Z to decay and have only 1.00 mg remaining is ____ years.

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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