Consider the reaction: CH3 OH(g) ⇌CO(g)+2 H2(g) Calculate ΔG for this reaction at 25^∘ C under t

Consider the reaction: CH3 OH(g) ⇌CO(g)+2 H2(g) Calculate ΔG...

Consider the reaction: $$\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$ Calculate $\Delta G$ for this reaction at $25^{\circ} \mathrm{C}$ under the following conditions: $P_{\mathrm{CH}_{3} \mathrm{OH}}=0.855 \mathrm{~atm}$ $P_{\mathrm{CO}}=0.125 \mathrm{~atm}$ $P_{\mathrm{H}_{2}}=0.183 \mathrm{~atm}$

Consider the reaction:
$$\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$
Calculate $\Delta G$ for this reaction at $25^{\circ} \mathrm{C}$ under the following conditions:
$P_{\mathrm{CH}_{3} \mathrm{OH}}=0.855 \mathrm{~atm}$
$P_{\mathrm{CO}}=0.125 \mathrm{~atm}$
$P_{\mathrm{H}_{2}}=0.183 \mathrm{~atm}$

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic potential that indicates the maximum amount of work obtainable from a system at constant temperature and pressure. It helps determine the spontaneity of a process, with a negative ?G indicating a spontaneous reaction and a positive ?G indicating a non-spontaneous one. This concept is central to understanding chemical equilibrium and reaction feasibility.

Standard Gibbs Free Energy Change

The standard Gibbs free energy change (?G°) refers to the change in free energy when reactants in their standard states (usually 1 atm for gases) transform into products. ?G° serves as a reference point in thermodynamic calculations and is used alongside non-standard operating conditions to determine the actual free energy change of a reaction.

Reaction Quotient

The reaction quotient (Q) is a dimensionless number that provides a snapshot of a reaction’s progress at any given moment by relating the current activities (or partial pressures/concentrations) of products and reactants according to their stoichiometric coefficients. It is used to assess how far a reaction is from equilibrium and to calculate the Gibbs free energy under non-standard conditions.

Thermodynamic Equation for Free Energy

The relationship ?G = ?G° + RT ln Q is fundamental in chemical thermodynamics. This equation connects the free energy change under non-standard conditions to the standard free energy change, incorporating the effects of temperature (T) and the reaction quotient (Q) through the gas constant (R). It allows prediction of reaction spontaneity under varying conditions.

Partial Pressures and Activity in Gaseous Systems

In gas-phase reactions, the partial pressure of a gas can be used as a measure of its activity when the gas behaves ideally. These partial pressures, normalized to a standard pressure (typically 1 atm), are used in the calculation of the reaction quotient (Q), which in turn influences the Gibbs free energy change under non-standard conditions.

Transcript

00:01 In this question we've been given a reaction in which ch3 or h forms co and 2h2.

00:12 And we've been asked to determine the overall gives energy change of this reaction.

00:19 And we know by definition this is equal to the standard gives energy change plus rt lean q.

00:31 And if we are to look at qp, this is equal to.

00:35 To the partial pressure of the products coh2 divided by pch3oh.

00:47 So remember we have to raise these into to their stoichiometric coefficients in this reaction and hydrogen is raised.

00:55 Hydrogen is multiplied by a stoichiometric coefficient of two.

00:58 So we have to raise or to square its partial pressure in the qp expression.

01:03 This is more like an equilibrium constant so looking at the enthalpy change rather the gibbs standard end up change this is going to be equal to we are looking at the sum of the gibbs the standard gives energy changes or formation of the products minors here we are looking at the standard gives energy change minus that of the reactants and remember we also have to include the stoichiometric coefficients because these values from our appendices or our tables are given in per mole so we always have to include the stoichiometric coefficients so if we are to look at this reaction this is going to be our reactants and this is going to be our products so we are saying products minus the reactants and if we are to substitute this we have delta the standard gives energy change being equal to one mole of the product which is is methanoe minus 37 137 plus 2 by 0 rather this is the product which is co minus that of hydrogen hydrogen is a pure element and understand that condition this is going to be 0 minus that of ethanol of metanoff which is equal to negative 1 mole of methanol multiplied by negative 16 2 .3.

02:45 So the standard gives energy change is going to be equal to 25 .1 and this is in kilojoules.

02:53 Now moving on to this formula that we add here...

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