段友大集合
范文一：标准平衡常数表达式的推导
标准平衡常?数表达式的?
推导
为讨论溶液?体系和多相?体系的平衡?，我们需要首?先引入一个?热力学函数?:化学势,。化学势是等?熵等容过程?每单位物质?量变化所引?起的体系内?能变化量，也是等温等?压过程每单?位物质量变?化所引起的?体系自由能?变化量，定义为:
(1) 上式中，S、V为熵和体?积，ni为体系?第i个组分?的物质量。 化学势是一?个强度量，即体系在平?衡时，所有子体系?或组分的化?学势都相等?。
(2)
其中，上标表示不?同的相。
对于单组分?体系，
(3)
上式中的星?号(*)表示纯物质?。
因此，对于1 mol单一?组分理想气?体体系，在恒温条件? 下:
(4)
上式中下标?id代表理?想气体。
当压力升高?后，理想气体状?态方程不再?适用，应当使用v?an der Waals?方程。但是，这样会使上?述表达式复?杂化。因此，为保持上述?表达式的简?洁形式，Gilbe?rt Newto?n Lewis?引入一个名?词:逸度f (fugac?ity)，使上述方程?对于非理想?气体也能够?保持原有的? 简洁:
(5)
对于混合气?体体系，上式可写为?:
(6)
从(4)式与(3)式的比较可?以看出，对于理想气?体来说，逸度就是压?力。当体系压力?趋于无限小?时，有:
(7)
类似地，对于混合体?系，有:
(8) 其中，xi为第i?个组分的摩?尔分数，P为体系的?总压。 因此，非理想气体?的逸度与理?想气体的压?力一样与各?自体系的化?学势相联系?。逸度与压力?的关系可以?表达为:
(9)
其中，,数。 i为逸度系?
如果我们把?(5)式的两边积?分，就得到:
(10) 如果我们把?起始态定义?为标态，那么上式就?可改写为:
(11) 这里，我们引入活?度 a (activ?ity)。由于体系达?平衡时，不同相态的?化学势相等?，所以对于与?气相平衡的?溶液相:
(12)
于是得到:
(13) 与逸度相似?，活度与摩尔?浓度的关系?可以表示为 ?:
(14)
其中，,数。 i为活度系?
根据化学势?的定义，在恒温恒压?下，我们有:
(15) 和
(16) 对于1mo?l组分物质?的自由能变?化，上述两式又?可写为:
(17) 和
(18) 所以，对于气体和?溶液体系，体系的自由?能变化为:
(19)
和
(20)
上式中，,程式中各物?质的系数。 i为化学方?
从上述两式?也可以看出?，对于气液混?合体系aA?(aq) + bB(g) , cC(aq)，我们同样可?以得到:
(21)
进而有:
(22) 这就是气液?混和体系的?标准平衡常? 数。
Kc是平衡?浓度、Kp是平衡?压强，这个指平衡?时的状况，没有一般表?达式 Ksp是沉?淀溶解平衡?常数，等于离子浓?度幂的乘积?，例如Ksp?(AgCl)=[Ag+][Cl-]
Ksp[Fe(OH)3]=[Fe3+]*([OH-]^3) Ka是酸的?电离平衡常?数Ka(HAc)=[H+][Ac-]/[HAc] Kb是碱的?电离平衡常?数，算法与酸类?似
Kw是水的?离子积常数?，Kw=[H+][OH-]
298K，101kP?a条件下K?w=1.0*10^(-14)
范文二：标准平衡常数表达式的推导[整理版]
标准平衡常数表达式的推
导
为讨论溶液体系和多相体系的平衡，我们需要首先引入一个热力学函数:化学势,。化学势是等熵等容过程每单位物质量变化所引起的体系内能变化量，也是等温等压过程每单位物质量变化所引起的体系自由能变化量，定义为:
(1)
上式中，S、V为熵和体积，n为体系第i个组分的物质量。 i
化学势是一个强度量，即体系在平衡时，所有子体系或组分的化学势都相等。
(2) 其中，上标表示不同的相。
对于单组分体系，
(3)
上式中的星号(*)表示纯物质。
因此，对于1 mol单一组分理想气体体系，在恒温条件下:
(4)
上式中下标id代表理想气体。
当压力升高后，理想气体状态方程不再适用，应当使用van der Waals方程。但是，这样会使上述表达式复杂化。因此，为保持上述表达式的简洁形式，Gilbert Newton Lewis引入一个名词:逸度 f (fugacity)，使上述方程对于非理想气体也能够保持原有的简洁:
(5) 对于混合气体体系，上式可写为:
(6) 从(4)式与(3)式的比较可以看出，对于理想气体来说，逸度就是压力。当体系压力趋于无限小时，有:
(7) 类似地，对于混合体系，有:
(8)
其中，x为第i个组分的摩尔分数，P为体系的总压。 i
因此，非理想气体的逸度与理想气体的压力一样与各自体系的化学势相联系。逸度与压力的关系可以表达为:
(9)
其中，,为逸度系数。 i
如果我们把(5)式的两边积分，就得到:
(10)
如果我们把起始态定义为标态，那么上式就可改写为:
(11) 这里，我们引入活度 a (activity)。由于体系达平衡时，不同相态的化学势相等，所以对于与气相平衡的溶液相:
(12)
于是得到:
(13) 与逸度相似，活度与摩尔浓度的关系可以表示为:
(14)
其中，,为活度系数。 i
根据化学势的定义，在恒温恒压下，我们有:
(15)
和
(16)
对于1mol组分物质的自由能变化，上述两式又可写为:
(17)
和
(18) 所以，对于气体和溶液体系，体系的自由能变化为:
(19)
和
(20)
上式中，,为化学方程式中各物质的系数。 i
从上述两式也可以看出，对于气液混合体系aA(aq) + bB(g) , cC(aq)，我们同样可以得到:
(21)
进而有:
(22)
这就是气液混和体系的标准平衡常数。
Kc是平衡浓度、Kp是平衡压强，这个指平衡时的状况，没有一般表达式
Ksp是沉淀溶解平衡常数，等于离子浓度幂的乘积，例如Ksp(AgCl)=[Ag+][Cl-]
Ksp[Fe(OH)3]=[Fe3+]*([OH-]^3)
Ka是酸的电离平衡常数Ka(HAc)=[H+][Ac-]/[HAc]
Kb是碱的电离平衡常数，算法与酸类似
Kw是水的离子积常数，Kw=[H+][OH-]
298K，101kPa条件下Kw=1.0*10^(-14)
范文三：平衡常数表达式
20076J. Phys. Chem. C 2009, 113, 20076–20080
Equilibrium Isotope Effect for Hydrogen Absorption in Palladium
Weifang Luo,*Donald F. Cowgill, and Rion A. Causey
Deptartment of Hydrogen and Metallurgical Sciences, Sandia National Laboratories 7011East A V enue, Li V ermore, California 94551
Recei V ed:June 15, 2009; Re V ised Manuscript Recei V ed:August 17, 2009
Absorption isotherms at 323K for the H -D -Pd system were measured by introducing H 2and D 2into Pd in sequence. The method using addition of isotopes to the system in sequence to investigate isotope exchange effects has not been previously reported. The equilibrium absorption pressure in the plateau region of the mixed-isotope system varies with the ratio of H/Din the solid phase. It lies between those of the single-isotope systems of H -Pd and D -Pd. Higher equilibrium pressures are associated with high D/Hratios in the solid phase. A model proposed previously (Luo,W.; Cowgill, D.; Causey, R.; Stewart, K. J. Phys. Chem., B 2008, 112, 8099) for mixed isotope hydride desorption, which correlates the equilibrium plateau pressure of the mixed H -D system with the fractions of D and H in the solid and the equilibrium plateau pressures of the single-isotope systems, is also successfully applied to absorption. When D 2is introduced into the H -Pd system in the plateau region, both the H -D exchange processes in the gas phase and net H (D)absorption take place. The former does not result in a total pressure change, but the latter creates a total pressure decrease. These reactions produce a D concentration increase in both the bulk Pd and the gaseous phase, as expected. Curiously, however, they also result in a counterintuitive small H concentration increase in bulk Pd and a decrease in gaseous H. Analogous results are obtained when the order of D 2-H 2introduction is reversed. In the plateau region, isotope displacement does not take place. Once in the -phase, isotope displacement does take place. The equilibrium isotope H -D partitions in the gas phase, H 2, HD, and D 2, are controlled by the equilibrium constant, K HD , and their equilibrium partitions among H and D between gas and bulk Pd are controlled by the separation factor, R .
1. Introduction
Hydrogen isotope effects attract research attention because of its importance for both fundamental and technical reasons. 1-13The most prominent equilibrium hydrogen isotope effect is observed for the hydrogen -Pd system. The hydrogen isotope effect observed from the absorption/desorptionisotherms is of interest since the isotherms of mixed isotopes deviate from those of the single isotopes, which provide useful information for understanding the mechanism of isotope exchange. One of the potential applications of the hydrogen isotope exchange is for heavy hydrogen isotope enrichment, and this requires an understanding of the mechanism and patterns of the exchange over a wide range of hydrogen concentrations in Pd, including all R , R + , and phases.
Sieverts et al. reported absorption isotherms for H -D -Pd at the ratios of P H 2/P D 2) 1:1and 1:3and the isotherms in the subsequent desorption at a temperature of 373K. 14The H/Dratios in the gas and solid phases, however, were not reported. The changing slope in these isotherms in the R- phase regions is obvious, but no discussion was given as to its origin.
Desorption isotherms at 323K for mixed Pd hydrides, Pd(Hx D 1-x ) y (0
*Corresponding author. Phone:(925)294-3729. Fax:(925)294-3410. E-mail:wluo@sandia.gov.
Isotope exchange in the H -D -Pd system takes place on the Pd surface, resulting in isotope composition variations in both the gas and solid phases before the system reaches equilibrium. The following equations describe the exchange processes:
H 2+D 2S 2HD H 2+D s S HD +H s HD +D s S H s +D 2
(1)(2)(3)
Here the subscripts “g”and “s”denote the quantities in gas and solid phases, respectively, and H g ) P H 2+(1/2)P HD , D g ) P D 2+(1/2)P HD . In this article, K HD ′and R ′are introduced to denote the nonequilibrated quantities of P HD 2/P H 2P D 2and D g /D s /H g /H s , respectively. When a system is at equilibrium, K HD ′) K HD and R ′) R .
Previous experimental results of H -D exchange on a clean Pt surface and in -phase Pd 14indicate that the equilibrium of eq 1is rapidly achieved; that is, P HD 2/P H 2P D 2) K HD . The exchanges in eqs 2-3in -Pd produce isotope composition variations in both gas and bulk Pd but do not result in a total pressure rise or fall. 14The observed equilibrium values 14are close to those reported in the literature. This con?rmsthat R determines the equilibrium partitions of H and D between the gas and solid phases; that is, H g , H s , D g , and D s , whereas K HD determines the equilibrium partition of H and D among the three species, P H 2, P HD , and P D 2, in the gas phase.
10.1021/jp905614xCCC:$40.75 2009American Chemical Society
Published on Web 10/21/2009
Hydrogen Absorption in Palladium J. Phys. Chem. C, Vol. 113, No. 46, 2009
20077
Figure 1. (a)H 2-D 2absorption pro?lesat 323K. The blue arrow indicates the time when the ?rstD 2dose was introduced, and the brown arrow indicates the time the plateau region ends. Pressures of H 2(blue),HD (pink),and D 2(green)and K HD ′and R ′values (light-blueand red, the right-hand y -axes) are included. (b)An insert for the area marked by the square in panel a.
For a system containing a very small amount of Pd in a large volume chamber, the absorption of hydrogen isotopes in bulk Pd would be insigni?cant,and therefore, eq 1is the major exchange concern. For a system containing a large amount of Pd in a small volume chamber, however, the major exchange activities are those described by eqs 2-3. In the current study the sample chamber volume and mass of Pd were selected in such a way that the ratio of the maximum amount of total hydrogen isotopes in the gas to that in bulk Pd was about 1:4at a total pressure of 1.5×105Pa and, therefore, the exchange activity involving isotope concentration variations in both the gas and solid phases must be considered.
In addition to the isotope exchange processes, there are nonexchange processes, such as the net H 2or D 2absorption in bulk Pd:
H 2S 2H s D 2S 2D s
(4)(5)
A total gas pressure decrease results from these processes, in contrast to the processes in eqs 1-3in which no net gas pressure changes are produced.
Instead of introducing a mixed isotope gas to the Pd, H 2and D 2were introduced here in sequence; that is, one isotope was introduced to the plateau region before the other isotope was introduced. This caused the isotope concentration variations in the gaseous and solid phases to be more obvious and easily identi?edfollowing the introduction of every dose of the second isotope.
2. Experimental Section
Palladium powder (2.3g, from Englehardt Inc.) was used in this study. The speci?csurface area of the sample was measured to be 0.2-0.5m 2/g,by the poresymmetry method, and therefore, its average particle size was ～0.6μm. The basic information about the sample and its pretreatment before data collecting were described elsewhere. 1,14The gases, H 2and D 2(highpurity
99.9995%from Matheson Inc.) were used for the isotherm measurements.
A Sieverts’apparatus was used to monitor the hydrogen absorption. The volume of the sample chamber for exchange was ～54mL at room temperature. Gas pressures in the sample vessel were monitored by MKS pressure gauges (MKSInstru-ments Inc.). The pressure in the system was in the range of 0to 1.5×105Pa during isotherm determinations.
The isotopic composition in the gas phase of the sample vessel was monitored by a residual gas analyzer, RGA-200(StanfordResearch Systems Inc.). A minimal amount of gas from the sample vessel was sent to the RGA by a ?ow-restrictedvalve as described elsewhere 1to ensure that the gas pressure in the RGA remained below 6×10-4Pa, as required by the RGA and to ensure the gas composition or pressure in the sample vessel was unaffected by the RGA sampling. Noise in the RGA measurement leads to errors in the pressure data, which affects the exchange calculations. The estimated magnitude of the error for the partial pressures from the RGA is <700pa or="" 2%of="" the="" readings,="" whichever="" was="">
The RGA signal was calibrated by pure hydrogen and deuterium separately, and their average was used as the calibration value for HD since HD is not commercially available. A linear correlation between the gauge pressures and RGA values was reported previously. 1
The sample was evacuated for 12h at 388K through a Turbo pump prior to an absorption measurement. Equilibrium pressures were recorded by pressure gauges during absorption. The partial pressures of three components in the gas phase s H 2, HD and D 2s were monitored by the RGA. The isotopic concentrations in the gas phase (i.e.,D g and H g ) were determined by the de?nitions;isotope concentrations in the solid phase (i.e.,D s and H s ) were calculated by the variations of H g and D g during exchange using the ideal gas law. 1
3. Results and Discussions
3.1. Absorption Pro?les.Figure 1a shows an example of an absorption pro?lein which 7doses of H 2were introduced initially followed by 12doses of D 2. Figure 1b is an enlarged area of Figure 1a marked by the square frame. The blue
arrow
20078J. Phys. Chem. C, Vol. 113, No. 46, 2009indicates the time when the ?rstD 2dose was introduced, and the brown arrow indicates the time when the system reached the end of the pressure plateau region. All partial pressures for the three gas components s H 2(blue),HD (pink),D 2(green)s and the sum of their pressures (total,brown) are included and read by the axis on the left.
From the observed pressure values in each dose, H g , D g , H s , D s , K HD ′, and R ′can be calculated, and their values are included in Figure 1. It can be seen that the R ′reaches its equilibrium value at the end of each dose of D 2introduction, and K HD ′also reaches equilibrium, although it is larger than its value of 3.3at 323K reported in the literature. 11This is believed to result from the extremely low values of P H 2(Figure1a).
It can be seen from the de?nitionsof K HD and R that the R values are more accurate than those of K HD since P H to calculate R . H 2is used to calculate K HD while H g is used g is the sum of P H 2and 1/2P HD , and therefore, errors from the measurement are much smaller than for P H 2, especially when P H 2values are below the accurate range of the pressure gauge (seeFigure 1a for the time period of 2500-3400s). The K HD values will not be included in the discussion which follows, since it is always expected to be at equilibrium due to the catalytically active Pd surface. The accuracy of K HD and R have been discussed more elsewhere. 14The only experimental K HD values in the literature are for Pt at 293K 15and for Pt and Pd at the temperature range of 173-298K. 14The commonly referred to K HD values are from those calculated by Urey’smodel. 10
It can be seen from Figure 1that HD appears and increases as soon as a dose of D 2enters the sample chamber, indicating the gas phase exchange is taking place (eq1). In the plateau region, the H 2pressure decreases, and the HD and D 2pressures increase upon the introduction of each dose of D 2. The variations in the three gas components result in a H g decrease and a D g increase (H g and D g are shown in Figure 3). It can also be seen that the total pressure (brownline) decreases following each dose of D 2, indicating a net H/Dabsorption takes place, corresponding to eqs 4-5, along with the exchange, corre-sponding to eqs 1-3. All these reactions in the plateau region result in a net increase of D g in the gas phase and of H s and D s in the solid phase but a net decrease of H g .
Summarizing the isotope concentration variations in the plateau region, it can be seen that D g and D s increase upon D 2introduction, as expected; however, the small H g decrease and H s increase are somewhat counterintuitive. D 2introduction results in a larger amount of net D-absorption in bulk Pd, as expected, and that does not result in H-desorption from the bulk Pd but, instead, produces a small amount of H-absorption to maintain the isotope ratio required by R . The net H s increase results from the small decrease in H g needed to satisfy this condition. The increase in the D solid-to-gas ratio produces an increase in the H solid-to-gas ratio. In summary, the variations observed here in the gaseous and solid phases are dictated by the separation factor to maintain the equilibrium values of (D g /D s )/(H g /H s ) ) R .
Results for the case that doses of H 2are introduced to the D 2-Pd system in the plateau region (i.e.the reversed order of H 2-D 2introduction) are shown in Figure 2. Six doses of D 2were introduced initially, followed by seven doses of H 2. In the plateau region, H s , H g , and D s increase while D g decreases. The net results in the isotope concentration variations in the plateau region are such that D s increases slightly and D g decreases while both H s and H g increase, which is analogous to the case of the reversed order of D 2/H2introduction.
Luo et
al.
Figure 2. D 2-H 2absorption pro?lesat 323K. The blue arrow indicates the time when the ?rstH 2dose was introduced. All symbols are assigned the same as in Figure 1.
Once the system reaches the -phase, the total pressure (brownline) during exchange does not change essentially, and H 2and HD start to increase while D 2decreases. This indicates the exchanges corresponding to eqs 1-3take place. The results in this region are more straightforward, and a full discussion was given previously. 14
3.2. Isotopic Equilibrium Pressures in Gas Phase. Figure 3shows the absorption pressure -composition isotherms for mixed isotopes in Pd at 323K. Two isotherms of single-isotope systems, H -Pd (blueline) and D -Pd (greenline), are included (markedas H 2and D 2) for comparison. The yellow diamonds are for the equilibrium pressure values at the end of each dose for the mixed-isotope runs measured by the pressure gauge. The green triangles and the blue squares are for D g and for H g , respectively, and they are obtained from the RGA monitor. The closed brown circles are the sum of H g and D g . In Figure 3a, the ?rst?vedoses introduced to the system were H 2only; the later doses were D 2only. The pink arrow indicates the composition where the input gas switches from H 2to D 2. It can be seen that the ?rst?vepoints of the isotherm fall onto the isotherm of H 2-Pd, as expected. For the later doses, the eq-uilibrium pressure at the end of each dose, read from the gauge, increased upon every D 2addition, deviating from the one for H 2-Pd, although it never exceeds the equilibrium pressure values of the single-isotope system of D 2-Pd. It can be seen that the pressure values read from the gauge (yellowdiamonds) and those obtained from the RGA (?lledbrown circles) are reasonably close.
Figure 3b is similar to Figure 3a, except the order of H 2and D 2addition was reversed. The symbols are assigned the same for both parts a and b. It can be seen in Figure 3b that at equilibrium, the gauge pressure decreased after H 2introduction, but it was never lower than that of the H 2-Pd plateau pressure. The value of the separation factor, R , for a plateau region is determined by the following equation 5for a plateau region:
R ) (P o D 2/P o H 2) 1/2
(6)
where P H o 2and P D o 2are the equilibrium plateau pressures of the single-isotope systems, that is, H 2-Pd and D 2-Pd, at a given temperature. At 323K, P H o 2) 6.8×103Pa and P D o 104Pa, and therefore, the R value at 323K in the plateau 2) 3.9×region should be 2.1. The R values for the mixed system
calculated
Hydrogen Absorption in Palladium J. Phys. Chem. C, Vol. 113, No. 46, 2009
20079
Figure 3. Mixed-isotope isotherms at 323K. Isotherms for single-isotope (H-Pd and D -Pd) systems are included for comparison. (a)First ?vedoses of H 2addition, followed by doses of D 2addition. (b)First ?vedoses of D 2addition, followed by doses of H 2
addition.
Figure 4. H and D concentrations in the solid phase during mixed-isotope absorption in Pd. (a)For the case of H 2-?rst-then-D2doses. (b)For the case of D 2-?rst-then-H2doses.
from the experimental H g , D g , H s , and D s are plotted in Figure 3a and b as the green, ?lledcircles. It can be seen that the R values in the plateau region are close to 2.1.
A model (eq7) was proposed previously to correlate the equilibrium plateau pressure of the single-isotope systems and the pressure of the mixed-isotope system in desorption:1
P mix ) P H 2o f H +P D 2o f D
(7)
Here, f H and f D are the fractions of H and D in the solid, respectively; that is, f H ) H s /(H s +D s ), f D ) D s /(H s +D s ), and f H +f D ) 1. This model can also be applied to absorption. The results calculated using eq 7for the mixed-isotope systems for the two runs are shown in Figure 3as the red lines. It can be seen that the model-calculated values are very close to the experimental values.
3.2. Equilibrium Isotopic Composition in Bulk Pd. Figure 4shows the equilibrium isotopic concentrations in the solid phase after introducing each dose during absorption. Two parallel data sets (thetriangles and the diamonds) are included for both cases of H 2-?rst-then-D2(Figure4a) and D 2-?rst-
then-H 2(Figure4b). In Figure 4the data in diamonds are from the run whose gas phase data are shown in Figure 3. The pink arrows in Figure 4indicate the hydrogen contents where H 2/D2addition switches for absorption. In these ?gures,the x -axis stands for the sum of the isotopic contents in the solid, that is, (H s +D s ); the y -axis is for H s (bluesymbols/lines),D s (greensymbols/lines)or (H s +D s ) (brownsymbols), respectively. It can be seen that while H g decreases slightly upon D 2introduction into the plateau region (Figure3a), the H content in the solid appears to remain constant (Figure4a). The H s increase is too small to be shown in Figure 4a. In addition, the D absorption in bulk Pd does not lead to an H s decrease in the plateau region. Similarly, H absorption in bulk Pd does not lead to a D s decrease in the plateau region. Once the system is in the -phase region, the exchange results in an H s decrease following D 2addition and a D s increase following H 2addition, as expected. As mentioned above, the separation constant, R , is responsible for this behavior. Conclusions
Absorption isotherms of the H -D -Pd system at 323K were measured. The equilibrium absorption pressure in the
plateau
20080J. Phys. Chem. C, Vol. 113, No. 46, 2009region of a mixed-isotope system varies with the ratio of H/Din the solid phase. These plateau pressures lie between those of the single-isotope systems of H -Pd and D -Pd. Higher equi-librium pressures are associated with high D/Hratios in the solid phase. A model was proposed previously 1for the mixed isotope hydride desorption that correlates the equilibrium plateau pressure of a mixed H -D system with the fractions of D and H in the solid and the equilibrium plateau pressures of the single-isotope systems of H -Pd and D -Pd. This model also success-fully applies to the case of absorption.
H -D isotope exchange during mixed H/Dabsorption can be detected by isotope concentration variations in the gas and solid phases. When D 2is introduced to the H -Pd system in the plateau region, both the exchange processes in the gas phase and the net H/Dabsorption processes take place; the former does not result in a total pressure change, but the latter results in a total pressure decrease as the plateau pressure transitions from pure H -Pd toward pure D -Pd. These reactions result in D concentration increases in both bulk Pd and gaseous phases, as expected; however, they also result in a H concentration increase in bulk Pd and a decrease in the gaseous phase, which is somewhat counterintuitive. Analogous results are obtained when the order of D 2-H 2introduction is reversed. In summary, the introduction of isotope A to a system containing isotope B in the plateau region results in an absorption of A without displacement of B by A. When the system is in the -phase region, adding isotope A to the system containing isotope B results in the absorption of the isotope A along with the displacement of B by A, keeping the total pressure constant in the system. In a nonequilibrated mixed H -D system, the isotope concentrations vary in such a way that P HD 2/(P H 2P D 2) and (D g /D s )/(H g /H s ) reach their equilibrium values, K HD and R , respec-tively. It is possible to drive out isotope A by using isotope exchange with isotope B if the system is in the -phase.
Luo et al.
However if the system is in the plateau region, it is necessary to introduce enough of isotope B to convert the system to the -phase before isotope A will be released to the gas phase. Acknowledgment. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’sNational Nuclear Security Administration under Contract DE-AC04-94AL85000. W. Luo thanks Prof. T. B. Flanagan at University of Vermont for valuable suggestions and advice. The authors thank Mr. K. Stewart for technical support for experimental setup design. References and Notes
(1)Luo, W.; Cowgill, D.; Causey, R.; Stewart, K. J. Phys. Chem., B 2008, 112, 8099.
(2)Lewis, F. A. The Palladium Hydrogen System ; Academic Press:London, NY, 1967.
(3)Flanagan, T. B.; Oates, W. A. Annu. Re V . Mater. Sci. 1991, 21, 269.
(4)Wicke, E.; Brodowsky, H. Hydrogen in Palladium and Palladium Alloys ; Topics in Applied Physics, Vol. 29; Springer:Berlin, Heidelberg, 1978.
(5)Andreev, B. M.; Magomedbekov, E. P.; Sicking, G. Interaction of Hydrogen Isotopes with Transition Metals and Intermetallic Coumponds , Kuhn J., Eds.; Springer:New York, 1996; ISBN 3-540-58369-6.
(6)Brodowsky, H.; Repenning, D. Z. Phys. Chem. NF, Bd. 1979, 114, 141.
(7)Wicke, E.; Nernst, G. Ber. Bunsenges, Phys. Chem. 1964, 68, 224. (8)Brodowsky, H. Z. Phys. Chem. N, Bd. 1965, 44, 129. (9)Sicking, G. Z. Phys. Chem. NF 1974, 93, 53.
(10)Urey, H. C.; Rittenberg, D. J. Chem. Phys. 1933, 1, 137. (11)Folts, G. W.; Melius, C. F. J. Catalyst 1987, 108, 409.
(12)Leardini, F.; Fernandez, J. F.; Bodega, J.; Sanchez, C. J. Phys. Chem. Mater. 2008, 69, 116.
(13)Sieverts, A.; Danz, W. Z. Phys. Chem. 1937, 38B , 46.
(14)Luo, W.; Cowgill, D.; Causey, R. J. Phys. Chem. B , 2009, 113, 12978.
(15)Gentsch, V. H. Z. Phys. Chem., NF, Bd. 1962, 35S , 85.
JP905614X
范文四：EQILIBRIUM CONSTANT EXPRESSION平衡常数表达式
EQUILIBRIUM CONSTANT EXPRESSION
LAW OF MASS ACTION / LAW OF CHEMICAL EQUILIBRIUM
Consider the following general equation aA + bB ?cC + dD cdabThe equilibrium expression is K(eq) = [C] [D] / [A] [B]
K(eq) is called the equilibrium constant. If the temperature changes, so will the K(eq).
The K(eq) for the reverse reaction will also be a constant and will be 1/K.
By convention, K(eq) = conc products / conc reactants The value of K is found by experiment
The units will vary but are often omitted
When the concentration of one of the reactants changes, the K(eq) value determines the amount of shift as the new concentrations must produce the same equilibrium constant.
The K(eq) value is known for many reactions at recommended temperatures.
If K(eq) is very small, the reactants are favored.
If K(eq) is very large, the products are favored
If K(eq) is close to 1, we have about the same amount of reactants and products at
equilibrium, neither is favored.
Only substances whose concentrations can vary are included in the expression.
Solids and pure liquids have a constant concentration at a given
temperature
and are not part of the expression. The position of equilibrium is not altered by
the amount of solid or liquid present but they must be present in the system.
Homogeneous equilibrium reaction-- All reactants and products in
same phase.
Heterogeneous equilibrium.-- Not all reactants and products in same phase
K (reverse) = 1/ K (forward) (reciprocal rule)
If Equation 3 = Eq 1 + Eq 2 Then K 3 = K 1 x K 2 ( multiple rule)
If we double an equation, the K value is squared (coefficient rule – If an equation is multiplied by N, the Keq is raised by a factor of N)
Example: 2NO(g) + O(g) ?2NO(g) 2222K(eq) = [NO] / [NO][O] 222= 2.6 x 10 at 725?C
224NO(g) + 2O(g) ?4NO(g) K(eq) = (2.6 x 10) 22
23Example N(g) + 3H(g) ?2NH(g) K(eq) = [NH]/ [N] [H] 2233222K(eq) = 6.3 x 10 at 200?C
322NH(g) ?N(g) + 3H(g) K(eq) = [N] [H]/[NH] 3222232K(eq) = 1/6.3 x 10 at 200?C
+2+Example: Zn(s) + 2Ag (aq) ?2Ag(s) + Zn(aq) 2++2K(eq) = [Zn] / [Ag]
-+Example: HO + NH(g) ?NH(aq) + OH(aq) 2(l)344+-K(eq) = [NH] [OH] / [NH] 3
SPECIAL CONSTANTS Kw Ka Ksp Kb
Kw ---- For the ionization of water Ka ---- For the ionization of acids in water Ksp ---- For the ionization of ionic compounds in water. (Called the
solubility
product)
Kb ---- For the ionization of bases in water +-H2O(l) ?H(aq) + OH(aq)
+--14Kw = [H] [OH] = 1.0 x 10 at 25?C
范文五：使用标准平衡常数表达式时要注意哪些问题【精品文档-doc】【精品文档-doc】
使用标准平衡常数表达式时要注意哪些问题?
一?1) 严格地讲～K表达式都应使用反应物和产物的活度(activity)而不是浓度。活度(a)与浓度之间的关系是:
a (反应物或产物)= γc (反应物或产物)
γ叫活度系数。理想溶液的γ=1～实际溶液的γ,1。活度是校正后的浓度, 也可看做是有效浓度。由于不涉及严密的理论处理～本教材的有关讨论中均使用浓度而不用活度。
2) 纯固体的浓度、纯液体的浓度和稀溶液中的浓度不出现在标准平衡常数表达式中。例如主篇式(3.14)讨论过的那个CaCO分解反应: 3
CaCO(s) CaO(s) + CO(g) 32
该反应的标准平衡常数表达式本应为:
一一?? {p(CO)/p}〃{p(CaO)/ p} 2 一? K= ———————————— 一? {p(CaCO)/ p} 3
一一??但化学上总是表达为为: K= {p(CO)/p} 2
作为纯液体, HO的蒸汽压只决定于温度, 一杯水的蒸汽压不会因为剩下半杯而减小。2
上述系统中的固相由独立存在的纯CaCO和独立存在的纯CaO微晶组成, 各自的分压具有3
与纯液体完全相同的特征。您不妨这样理解: 纯固体分压这样的常数已经归入标准平衡常数
-3一?本身。同样, 稀的水溶液中HO的浓度近似于常数(55.5 mol?dm)～也可理解为已归入K。 2
一一??3) K表达式要与化学方程式相对应。这是因为方程式写法不同时K表达式也不同。例如由H和O生成HO的化学方程式可以有两种写法: 222
2 H(g) + O(g),2 HO(g) 222
H(g) + (1/2)O(g),HO(g) 222
’’’一一??如果分别用K和K表示其标准平衡常数～则有:
2一一??{p(HO)/p} {p(HO)/p} 22’’’一一??K= ———————————— K= ———————————— 21/2一一一一????{p(H)/ p}〃{p(O)/ p} {p(H)/p}〃{p(O)/ p} 2222
它们之间的关系是:
’1/2’’一一?? K= (K)
一般说来～如果反应方程式中的化学计量数乘以n～对应的标准平衡常数应等于原标准平衡常数的n次方。
4) 如果同一平衡系统的反应物和产物换位, 标准平衡常数应取原标准平衡常数的倒数。例如对NO～O和NO构成的系统而言, 下列两个反应方程式从平衡观点没有任何差别: 22
2 NO(g) + O(g) 2 NO(g) 22
2 NO(g) 2 NO(g) + O(g) 22
’’’一一??如果用K和K表示各自的标准平衡常数, 您会发现它们之间互为倒数关系:
’’’一一?? K = 1/ K
5) 如果总反应的反应方程式可由两个或两个以上反应的方程式相加得到, 总反应方程式的标准平衡常数则等于各组成反应方程式标准平衡常数之乘积。例如反应
2 NO(g) + O(g),NO(g) 224
一?的K应为
2一? {p(NO)/p} 24
一? K= ———————————— 2一一?? {p(NO)/ p}〃{p(O)/p} 2
该反应可能通过两步机理完成:
2 NO(g) + O(g),2 NO(g) 22
2 NO(g),NO(g) 224
其标准平衡常数分别为:
2一一??{p(NO)/p} O)/p} {p(N224’’’一一??K= ———————————— K= —————— 22一一一???{p(NO)/ p}〃{p(O)/ p} {p(NO)/ p} 22
’’’一一一???不难发现～将K和K相乘可得K:
一?由于从总反应方程式得到K时并未假定反应分步进行的机理～从而导致一个十分重要的概念:标准平衡常数与反应分多少步完成(即反应机理)无关。不论NO与O生成NO的224反应是通过两步还是通过200步完成～您都可以根据总反应的化学方程式放心地写出标准平衡常数表达式。我们根据反应方程式中的计量系数写出了速率定律, 但是要以反应方程式表达的反应是元反应为前提。
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