Equilibrium constant without units

Notice that no units are given for either in Table 15.1 or in the calculation we just did using Experiment 1 data. It is common practice to write equilibrium constants without units for reasons that we address later in this section. 

In real systems, activities are also ratios that have no units. Even though these activities may not be exactly numerically equal to concentrations, we will ignore the differences. All we need to know at this point is that activities have no units. As a result, the thermodynamic equilibrium constants derived from them also have no units. It is therefore common practice to write all types of equilibrium constants without units, a practice that we adhere to in this text. In more advanced chemistry courses, you may make more rigorous distinctions between concentrations and activities. 

Substitute these values into the equilibrium expression for catalytic methanation. (The expression was obtained in Example 15.2.) Although until now we have consistently carried units along with numbers in calculations, it is the usual practice to write equilibrium constants without units. We will follow that practice here. Substitution of concentrations into the equilibrium-constant expression gives... 

Think About It When putting the equilibrium concentrations into the equilibrium expression, we leave out the units. It is common practice to express equilibrium constants without units. We wUl examine the reason why in Section 15.5. 

We can write a reactant quotient at any point during the reaction, but the most meaningful point is when the reaction has reached equilibrium. At equilibrium, the reaction quotient becomes the equilibrium constant, Kc (or Kp if gas pressures are being used). We usually express this equilibrium constant simply as a number without units since it is a ratio of concentrations or pressures. In addition,... 

SOLUTION The chemical equation and the expression for the equilibrium constant Kc are given in reaction C and Eq. 12, respectively. We substitute the equilibrium molar concentrations (without their units) into the expression for Kc ... 

Values of Kc are generally reported without units because the concentrations in the equilibrium constant expression are considered to be concentration ratios in which the molarity of each substance is divided by its molarity (1 M) in the thermodynamic standard state (Section 8.6). Because the units cancel, the concentration ratios and the values of Kc are dimensionless. For experiment 1 in Table 13.1, for example,... 

Finally, let us define the Henry s law constant, which is the ratio of the equilibrium concentration of a compound in solution to the equilibrium concentration of that compound in the gas phase over that solution. It is usually given as A h- This constant can be given in one of two ways with and without units. We will use the version with units here ... 

In this chapter we will often retain the (apparent) units for Kp or K to remind ourselves which reference state is being used and to facilitate conversions between K and Kp. However, in the remainder of the text, the value of equilibrium constants usually will be given without units. 

The convention we follow in this book is to describe chemical equilibrium in terms of the thermodynamic equilibrium constant K, even when analyzing reactions empirically. Consequently, for gaseous reactions we will state values of K without dimensions, and we will express all pressures in atmospheres. The Pref factors will not be explicitly included because their value is unity with these choices of pressure unit and reference pressure. Following this convention, we write the mass action law for a general reaction involving ideal gases as... 

Substituting the numerical values (without units) into the equilibrium expression gives the value of the equilibrium constant. 

Note that in the preceding discussion, the equilibrium constant was given without units. In certain cases the units are included when the values of equilibrium constants are given, and in other cases they are omitted. We will not discuss the reasons for this. We will omit the units in this text. 

It is very important to note at this point that the equilibrium constants are customarily given without units. The reason for this is beyond the scope of this text, but it involves corrections for the nonideal behavior of the substances taking part in the reaction. When these corrections are made, the units cancel out and the corrected K has no units. Thus we will not use units for K in this text. 

The standard state to which conventional thermodynamic equilibrium constants refer is that of unit mole fraction for each solid phase component in a reaction and unit molality without coulomb interactions for each aqueous phase ion in a reaction. See p. 32 in G. Sposito, op. cit. ... 

By convention, equilibrium constant values are given without units. 

You may wonder why equilibrium constants are reported without units. The equilibrium constant is related to the kinetics of a reaction as well as to the thermodynamics. (We explore this latter connection in Chapter 19.) Equilibrium constants derived from thermodynamic measurements are defined in terms of activities rather than concentrations or partial pressures. 

Because of the use of activities, the equilibrium constant has no units the values we put into A). are numerically equal to molar concentrations but are dimensionless, that is, they have no units. Therefore, calculations involving equilibrium are frequently carried out without units we will follow that practice in this text. 

In order to calculate a standard value of the equilibrium constant, K, for a reaction the values of the concentrations entered in the equilibrium expression must numerically be in moldm. Strictly speaking the values entered diould be activity values rather than concentrations. For gases and relatively dilute solutions the concentration values are sufficiently close to the activity values that their use does not introduce any significant errors into the calculation. Since the activity values for substances are simply a number - they do not have any units - it follows that coxy value will also simply be a number without units no matter which reaction you are studying. Certainly in the IB examination you will not be asked for any units relating to values. 

We have said that it is common to disregard units and write equilibrium constants as dimensionless quantities. The reason is as follows Prior to being used in an equilibrium expression, each molar concentration is divided by a reference concentration of 1M, and each partial pressure is divided by a reference pressure of 1 atm. The reference concentration (1 M) and reference pressure (1 atm) are known as the standard states for aqueous and gaseous species, respectively. This cancels the units without changing the value of the concentration or pressure in question. The dimensionless result of dividing a concentration by a reference value is called the activity. Activities commonly are used by chemists in place of concentrations, but a detailed discussion of activities is beyond the scope of this book. Using as an example the equilibrium between N2O4 and NO2,... 

In each case, dividing by the reference value eliminates the units without changing the numerical value of the result. We will not show the division by reference values explicitly, but you should realize that this is the reason why there are no units associated with equilibrium constants. 

Jacobson and Stockmayer analyzing the density of distribution of segments of linear polymer formulated a theory relating the distribution function of the end-to-end veaor r for linear polymer composed of x units (Wx(r)), per unit range in r, with the equilibrium constant of cyclization for systems without ring-strain and other enthalpic factors (equilibrium governed only by entropic factors) ... 

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