1. For the methanol synthesis reaction \[ \text{CO (g) + 2 H}_2 \text{(g) } \rightleftharpoons \text{ CH}_3\text{OH (g)} \]the equilibrium constant is given by: \[ \ln K = 11.988 + \left(\frac{9143.6}{T}\right) - 7.492 \ln T + 4.076 \times 10^{-3} T - 7.161 \times 10^{-8} T^2 \]where \( T \) is in K. Estimate the standard heat of reaction at 473 K using the above relation.

Given that, CO(g) + 2H2(g) → CH3OH(g) Equilibrium constant: lnK = 11.988 + 9143.6T - 7.492 lnT + 4.076 × 10-3T - 7.161 × 10-8T2 It is required to calculate the standard heat of reaction at 473 K.HrxnRT2 = dlnKdTHrxnRT2 = ddT11.988 + 9143.6T - 7.492 lnT + 4.076 × 10-3T - 7.161 × 10-8T2HrxnRT2 = 0 - 9143.6T2 - 7.492T + 4.076 × 10-3 - 2 × 7.161 × 10-8THrxn = -9143.6T2 - 7.492T + 4.076 × 10-3 - 14.322 × 10-8T × RT2Hrxn = -9143.64732 - 7.492473 + 4.076 × 10-3 - 14.322 × 10-8 × 473 × 8.314 Jmol.K × 4732Hrxn = -0.041 - 0.016 + 4.076 × 10-3 - 6.774 × 10-5 × 8.314 Jmol.K × 4732Hrxn = -0.053 × 8.314 Jmol.K × 4732Hrxn = -98584.39 JmolHrxn = -98.584 KJmolAnswer: The standard heat of reaction at 473 K = -98.584 KJ/mol negative sign indicates heat is released during the reaction.

Answered: 1. For the methanol synthesis reaction…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

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1. For the methanol synthesis reaction
\[ \text{CO (g) + 2 H}_2 \text{(g) } \rightleftharpoons \text{ CH}_3\text{OH (g)} \]
the equilibrium constant is given by:
\[ \ln K = 11.988 + \left(\frac{9143.6}{T}\right) - 7.492 \ln T + 4.076 \times 10^{-3} T - 7.161 \times 10^{-8} T^2 \]
where \( T \) is in K. Estimate the standard heat of reaction at 473 K using the above relation.

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