Chapter 18, Problem 95SCQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# “Heater Meals” are food packages that contain their own heat source, lust pour water into the heater unit, wait a few minutes, and voila! You have a hot meal.Mg(s) + 2 H2O(ℓ) → Mg(OH)2(s) + H2(g) (a) Confirm that this is a product-favored reaction at equilibrium at 25 °C. (b) What mass of magnesium is required to produce sufficient energy to heat 225 mL of water (density = 0.995 g/mL) from 25 °C to the boiling point?

(a)

Interpretation Introduction

Interpretation:

It should be predicted that if the given reaction of magnesium with water is product-favoured.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrGo. It is related to entropy and entropy by the following expression,

ΔrGorHo-TΔrSo

It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

The sign of ΔrGo should be positive for a product-favored reaction. Thus, spontaneous reactions are referred to those that have negative free energy formation.

The heat q is related to the specific heat by the expression,

q = -mcΔT

Here, ΔT is the temperature change and m is the mass of the substance. c is the specific heat which is constant. The specific heat of water is 4.186 J/g °C.

Explanation

The value of ΔGo for the reaction of magnesium with water is calculated below.

Given:

Refer to Appendix L for the values of standard free energy values.

The given reaction is,

Mg(s) + 2H2O(l)Mg(OH)2(s)+H2(g)

The ΔrG° for Mg(OH)2(s) is 833.51 kJ/mol.

The ΔrG° for H2(g) is 0 kJ/mol.

The ΔrG° for Mg(s) is 0 kJ/mol.

The ΔrG° for H2O(l) is 237.15 kJ/mol.

ΔrG°fG°(products)fG°(reactants)=[[(1 mol Mg(OH)2(s)/mol-rxn)ΔfG°[Mg(OH)2(s)]+(1 mol

(b)

Interpretation Introduction

Interpretation:

The mass of magnesium needed to produce energy in order to heat 225mL from given temperature to its boiling point should be identified.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔrGo. It is related to entropy and entropy by the following expression,

ΔrGorHo-TΔrSo

It can be calculated in a similar manner as entropy and enthalpy.  The expression for the free energy change is:

ΔrG°fG°(products)fG°(reactants)

The sign of ΔrGo should be positive for a product-favored reaction. Thus, spontaneous reactions are referred to those that have negative free energy formation.

The heat q is related to the specific heat by the expression,

q = -mcΔT

Here, ΔT is the temperature change and m is the mass of the substance. c is the specific heat which is constant. The specific heat of water is 4.186 J/g °C.

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