Standard state of a gas

Standard State of a Gas The standard state for a gas is usually chosen as the 

Activity is a dimensionless quantity, and / must be expressed in kPa with this choice of standard state. It is inconvenient to carry f° = 100 kPa through calculations involving activity of gases. Choosing the standard state for a gas as we have described above creates a situation where SI units are not convenient. Instead of expressing the standard state as /° = 100 kPa, we often express the pressure and fugacity in bars, since 1 bar = 100 kPa. In this case, /0 — 1 bar, and equation (6.92) becomes4 

With the standard state expressed in this manner, the activity of the gas becomes the fugacity expressed in bars. We will usually follow this convention as we work with activities of gases. An added convenience comes from being able to relate fugacity to pressure through the fugacity coefficient p, 

when / and p are expressed in bars, activity is given by 

At low pressures, it is a good approximation to replace the activity of gases by the pressure (in bars). 

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As noted earlier, the standard state of a gas is the hypothetical ideal gas at 1 atmosphere and the specified temperature T. 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

Equation n. B. 19. gives the difference in free energy from the standard state of a gas at any temperature and pressure. The relationship of the entropy to the pressure is given by ... 

Water has an activity of 1 when Nw (see Eq. 2.8) is 1. The concentration of water on a molality basis (number of moles of a substance per kilogram of water for aqueous solutions) is then 1/(0.018016 kg mol-1) or 55.5 molal (m). The accepted convention for a solute, on the other hand, is that aj is 1 when yfj equals 1 m. For example, if yj equals 1, a solution with a 1 -m concentration of solute j has an activity of 1 m for that solute. Thus the standard state for an ideal solute is when its concentration is 1 m, in which case RT In a - is zero.2 A special convention is used for the standard state of a gas such as CO2 or O2 in an aqueous solution—namely, the activity is 1 when the solution is in equilibrium with a gas phase containing that gas at a pressure of 1 atm. (At other pressures, the activity is proportional to the partial pressure of that gas in the gas phase.)... 

We are already used to the concept of standard state in respect of pure solids, liquids and gases. The standard state of a liquid or solid substance, whether pure or in a mixture, or for a solvent is taken as the state of the pure substance at 298 K and 1 bar pressure (1 bar = 1.00 x 10 Pa) the standard state of a gas is that of the pure gas at 298 K, 1 bar pressure and exhibiting ideal gas behaviour. 

As noted above, the standard state of a gas is chosen to be the state of 1 mol of pure gas at 1 atm (0.1 MPa) pressure and the temperature of interest. One should thus realize that whenever a partial pressure P, appears in an expression such as Eq. (5.28), it is implicit that one is dealing with the dimensionless ratio, Pj/ atm. 

Standard Reference Material See certified reference material, standard solution A solution whose composition is known by virtue of the way that it was made from a reagent of known purity or by virtue of its reaction with a known quantity of a standard reagent, standard state The standard state of a solute is 1 M and the standard state of a gas is 1 bar. Pure solids and liquids are considered to be in their standard states. In equilibrium constants, dimensionless concentrations are expressed as a ratio of the concentration of each species to its concentration in its standard state. 

The standard state of a gas at 1 atm and working temperature is considered devoid of intermolecular interactions. Analogously in standard state of GSC at any temperature adsorbate-adsorbate interactions are absent there are only interactions of adsorbed molecules with the adsorbent surface. The selection of a given value for surface pressure in the standard state is arbitrary, as in selection of the pressure of 1 atm for a normal gas there is no correlation between the pressure of 1 atm and two-dimensional pressure. 

The standard state of a gas, however, is a hypothetical state in which the gas behaves ideally at the standard pressure without influenee of intermolecular forces. The properties of the gas in this standard state are those of an ideal gas. We would like to be able to relate molar properties of the real gas at a given temperature and pressure to the molar properties in the standard state at the same temperature. 

The reactant and product species for both the reduction half-reaction and the hydrogen oxidation half-reaction are specified to be in their standard states. Recall that the standard state of a gas is an ideal gas at 1 bar, a liquid is a 1 m ideal solution in the Henry s law sense, and a solid is the pure solid with an activity of 1. In terms of our shorthand notation, we can measure the standard potential of any reduction half-reaction with a standard hydrogen electrode (S.H.E.) ... 

The thermodynamic standard state of a substance is its most stable state under standard pressure (1 atm) and at some specific temperature (usually 25°C). Thermodynamic refers to the observation, measurement and prediction of energy changes that accompany physical changes or chemical reaction. Standard refers to the set conditions of 1 atm pressure and 25°C. The state of a substance is its phase gas, liquid or solid. Substance is any kind of matter all specimens of which have the same chemical composition and physical properties. 

In mixtures of real gases the ideal gas law does not hold. The chemical potential of A of a mixture of real gases is defined in terms of the fugacity of the gas, fA. The fugacity is, as discussed in Chapter 2, the thermodynamic term used to relate the chemical potential of the real gas to that of the (hypothetical) standard state of the gas at 1 bar where the gas is ideal ... 

The standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

The right-hand equality in Equation (10.10), which gives the molar free energy of a pure ideal gas, is of the same form as Equation (10.15), which gives the chemical potential of a component of an ideal gas mixture, except that for the latter, partial pressure is substituted for total pressure. If the standard state of a component of the mixture is defined as one in which the partial pressure of that component is 0.1 MPa, then... 

The reference temperature is usually 298.15 K (25°C). Where there is more than one allotrope, then the stable form of the solid is chosen. In spite of the definition of the standard state, it is occasionally convenient to speak of the standard state of the gas at 25°C for a substance which is actually liquid or solid at this temperature and a pressure of 1 atm water is a compound for which this is often done. 

We define the standard state of a liquid as ay = 1 and for gases as an ideal gas pressure of 1 bar, Pj = I- For ideal liquid solutions (activity coefficients of unity), we write ay = Cy so at chemical equilibrium... 

How does the change in Gibbs energy vary if we go from the standard state of a compound to some other state Consider a change of pressure in a gas. It is easy to show (see any thermodynamics text) that... 

Let the gas pressure that corresponds to adsorption equilibrium be denoted as p. The value of p for the standard state of a site is denoted as b and is called desorption pressure of the site (Section IV). Each site of a non-uniform surface is characterized by a certain b value or by an adsorption coefficient, a = l/b (for a given temperature). At adsorption equilibrium, the probability that a site is occupied... 

We define the standard state of a real gas so that Eq. (51) is general (i.e., so that it also applies to ideal gases). For ideal gases, the standard state is at 1.0 bar pressure. For real gases, we also use a 1.0-bar ideal gas as the standard state. We find the standard state by the two-step process shown in Fig. 6. First we extrapolate the real gas to very low pressure, where / —> P and the gas becomes ideal (Step I). We then convert the ideal gas to 1.0 bar (step II). The convenience of an ideal gas standard state is that it allows temperature conversions to be made with ideal gas heat capacities (which are pressure independent). Conversion to the real gas state is then made at the temperature of interest. 

Employing standard states of a single solute in a physical state of infinite dilution in the liquid stationary phase at the temperature and pressure of the system and a single solute in the perfect gas state at unit pressure and the temperature of the system for the solute in the stationary and in the gaseous phase, respectively, we obtain for the standard molar Gibbs function of sorption of solute i, AG°p(/) [19] ... 

In this example the standard heat of formation of H20 is available for its hypothetical standard state as a gas at 25°C. One might expect the value of the heat of formation of water to be listed for its actual state as a liquid at 1 bar or l(atm) and 25°C. As a matter of fact, values for both states are given because they are both frequently used. This is true for many compounds that normally exist as liquids at 25°C and the standard-state pressure. Cases do arise, however, in which a value is given only for the standard state as a liquid or as an ideal gas when what is needed is the other value. Suppose that this, were the case for the preceding example and that only the standard heat of formation of liquid H20 is known. We must now include an equation for the physical change that transforms water from its standard state as a liquid into its standard state as a gas. The enthalpy change for this physical process is the difference between the heats of formation of water in its two standard states ... 

This step is necessary because, by convention, the standard state of a real gas is actually the hypothetical state of the ideal gas at one bar. Allowance must be made for the difference between these two states in exact determinations. Since the enthalpy of an ideal gas is independent of pressure, the difference between its value and that of the real gas may be determined by integrating Eq. (1.13.17) between pressure 0 and pressure P. In general this value tends to be very small compared to the contribution from all other steps. 

The standard state for a gas is the ideal-gas state of the pure gas at tire standard-state pressure P° of 1 bar. Since tire fugacity of an ideal gas is equal to its pressure, /,-° = P° for each species/. Thus for gas-pliase reactions= fi/P°, etnd Eg. (13.10) becomes ... 

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