From 3aedd7eb87047daeed309927966a2260145aff69 Mon Sep 17 00:00:00 2001 From: oscryan Date: Wed, 2 Oct 2024 17:58:44 +0000 Subject: [PATCH] 24202 both books attempt --- modules/m68799/index.cnxml | 10 ++-- modules/m71835/index.cnxml | 120 +++++++++++++++++++++---------------- 2 files changed, 74 insertions(+), 56 deletions(-) diff --git a/modules/m68799/index.cnxml b/modules/m68799/index.cnxml index 86039fb..45e988c 100644 --- a/modules/m68799/index.cnxml +++ b/modules/m68799/index.cnxml @@ -39,17 +39,17 @@ QP = - PHI2 - PH2PI2=KP + PHI2 + PH2PI2=KP If the volume occupied by an equilibrium mixture of these species is decreased by a factor of 3, the partial pressures of all three species will be increased by a factor of 3: -Qp'= +QP'= (3PHI)2 3PH23 PI2= -9PHI2 +9PHI2 9PH2 PI2= -PHI2 +PHI2 PH2 PI2= QP diff --git a/modules/m71835/index.cnxml b/modules/m71835/index.cnxml index a7f8237..c05317b 100644 --- a/modules/m71835/index.cnxml +++ b/modules/m71835/index.cnxml @@ -35,57 +35,75 @@ M=nV=PRT and so changes in the partial pressures of any reactant or product are essentially changes in concentrations and thus yield the same effects on equilibria. Aside from adding or removing reactant or product, the pressures (concentrations) of species in a gas-phase equilibrium can also be changed by changing the volume occupied by the system. Since all species of a gas-phase equilibrium occupy the same volume, a given change in volume will cause the same change in concentration for both reactants and products. In order to discern what shift, if any, this type of stress will induce the stoichiometry of the reaction must be considered. At equilibrium, the reaction H2(g)+I2(g)⇌2HI(g) is described by the reaction quotient -Qp= - -P - - - HI - 2 - - - - -P - H2 - -P - I2 - -=KpIf the volume occupied by an equilibrium mixture of these species is decreased by a factor of 3, the partial pressures of all three species will be increased by a factor of 3: - -Qp' -= -(3PHI2)2 - 3PH2 - -3PI2 -= -9PHI29PH2PI2 -=PHI2 -PH2PI2=Qp=KpQp'=Qp=KpAnd so, changing the volume of this gas-phase equilibrium mixture does not result in a shift of the equilibrium.A similar treatment of a different system, 2NO2(g)⇌2NO(g)+O2(g), however, yields a different result: -Qp=PNO2PO2 -P(NO2)2 -= -KpQp' -= -(3PNO)2 -3 -PO2(3PNO2)2=9PNO23PO2 -9 - -P(NO2) -2 - - - -= -27PNO2PO2 - -P(NO2) -2 - -=3Qp>KpQp'=3Qp>KpIn this case, the change in volume results in a reaction quotient greater than the equilibrium constant, and so the equilibrium will shift left. + + QP + = + + PHI2 + PH2PI2=KP +If the volume occupied by an equilibrium mixture of these species is decreased by a factor of 3, the partial pressures of all three species will be increased by a factor of 3: +QP'= +(3PHI)2 +3PH23 +PI2= +9PHI2 +9PH2 +PI2= +PHI2 +PH2 +PI2= +QP +=KPQP +'=QP= +KP +And so, changing the volume of this gas-phase equilibrium mixture does not result in a shift of the equilibrium. +A similar treatment of a different system, 2NO2(g) ⇌ 2 NO(g) + O2(g), however, yields a different result: + + + QP= + PNO2 + PO2 + PNO22 + + + QP'= + + + (3 + PNO) + 2 + 3PO2 + + (3PNO2 + ) + 2 + + + =9PNO2 + 3PO2 + 9PNO22 + = + 27PNO2 + PO2 + 9 + + + + P + + NO + 2 + + + + 2 + + =3QP + > + KP + QP' + =3QP>KP + In this case, the change in volume results in a reaction quotient greater than the equilibrium constant, and so the equilibrium will shift left. These results illustrate the relationship between the stoichiometry of a gas-phase equilibrium and the effect of a volume-induced pressure (concentration) change. If the total molar amounts of reactants and products are equal, as in the first example, a change in volume does not shift the equilibrium. If the molar amounts of reactants and products are different, a change in volume will shift the equilibrium in a direction that better “accommodates” the volume change. In the second example, two moles of reactant (NO2) yield three moles of product (2NO + O2), and so decreasing the system volume causes the equilibrium to shift left since the reverse reaction produces less gas (2 mol) than the forward reaction (3 mol). Conversely, increasing the volume of this equilibrium system would result in a shift towards products. Check out this link to see a dramatic visual demonstration of how equilibrium changes with pressure changes.