Interpretation Introduction To determine: The volume of methane at 298 K and 1.00 atm . Explanation Given: The heat of combustion of CH 4 is 890.4 kJ / mol . The heat capacity of H 2 O ( l ) is 75 .2 J / ( mol .K) . The volume of water ( V ) is 1 L = 1000 mL . The pressure of the gas ( P ) is 1 atm . The initial temperature ( T i ) is 298 K . The final temperature ( T f ) is 373 K . The ideal gas constant ( R ) is 0.0821 L atm / ( mol . K) . Explanation: The density of water ( d ) is 1 g / m L . First calculate the mass of water ( m ) as follows: The mass of water is equal to the product of density and volume of water. m = d × V Substitute 1 g / m L for d and 1000 mL for V as follows: m = 1 g / m L × 1000 mL = 1000 g So, the mass of water is 1000 g . One kilogram is equal to thousand grams. Therefore, the mass of water is 1 kg . Now, calculate the number of moles of water ( n ) as follows: The molar mass of water ( M ) is 18.01 g / mol . The number of moles of water is the ratio of the mass of water and its molar mass. n = m M Substitute 18.01 g / mol for MM and 1000 g for m as follows: n = 1000 g 18.01 g / mol = 55.525 mol So, the moles of water is 55.525 mol . The process of conversion of water to water vapor involves two sequential steps. First is the conversion of water from 298 K to water at 373 K . The amount of heat is given as follows: q water ( 1 ) = n C p Δ T Δ T = T f − T i where q water is the amount of heat required, m is the mass of water, C p is the molar heat capacity at constant pressure, Δ T is the change in temperature, T i is the initial temperature of water, and T f is the final temperature of water. Substitute 75 .2 J / ( mol K) for C p , 55.525 mol for n , 373 K for T f and 298 K for T i as follows: q water ( 1 ) = 55

Chemistry: A Molecular Approach Selected Solutions Manual, Books a la Carte Edition

4th Edition

ISBN: 9780134554259

Author: Nivaldo J. Tro

Publisher: PEARSON

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Chapter 11, Problem 99E

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To determine: The volume of methane at 298 K and 1.00 atm.

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Chapter 11, Problem 98E

Chapter 11, Problem 100E

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Chapter 11 Solutions

Chemistry: A Molecular Approach Selected Solutions Manual, Books a la Carte Edition

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