Methane standard state

There are many ways to express the energy of a molecule. Most common to organic chemists is as a heat of formation, AHf. This is the heat of a hypothetical chemical reaction that creates a molecule from so-called standard states of each of its constituent elements. For example, AHf for methane would be the energy required to create CH4 from graphite and H2, the standard states of carbon and hydrogen, respectively. 

It has been proposed that if ammonia, methane, and oxygen gas are combined at 25°C in their standard states, glycine, the simplest of all amino acids, can be formed. 

These values of A Hr are standard state enthalpies of reaction (aU gases in ideal-gas states) evaluated at 1 atm and 298 K. 7VU values of A are in kilojoules per mole of the first species in the equation. When A Hr is negative, the reaction hberates heat, and we say it is exothermic, while, when A Hr is positive, the reaction absorbs heat, and we say it is endothermic. Tks Table 2-2 indicates, some reactions such as isomerizations do not absorb or liberate much heat, while dehydrogenation reactions are fairly endothermic and oxidation reactions are fairly exothermic. Note, for example, that combustion or total oxidation of ethane is highly exothermic, while partial oxidation of methane to synthesis gas (CO + H2) or ethylene (C2H4) are only slightly exothermic. 

You may wonder how a reaction, such as combustion of methane, can occur at 25°. The fact is that the reaction can be carried out at any desired temperature. The important thing is that the AH° value we are talking about here is the heat liberated or absorbed when you start with the reactants at 25° and finish with the products at 25°. As long as AH0 is defined this way, it does not matter at what temperature the reaction actually occurs. Standard states for gases are 1 atm partial pressure. Standard states for liquids or solids usually are the pure liquid or solid at 1 atm external pressure. 

Without performing any calculations, predict whether an increase or a decrease in entropy occurs for each of the following processes (a) combustion of methane (b) standard state formation of carbon dioxide (c) the coiling of two strands of DNA to form a double helix. 

The best choice for the standard hydrate is one that is well-characterized and not too different from the real state of the system. If the standard state is well-defined, small perturbations from this standard state can be accounted for correctly. With this in mind, we turn to the three most well-known hydrates of si, sll, and sH, namely methane, propane, and methane+neohexane. Note that the standard states for si, sll, and sH are the empty hydrate lattices of these and not the actual hydrates. Therefore for the reference hydrates, the activity coefficients for methane, propane, and methane + neohexane hydrates will be unity. 

We define the molar volume of the standard hydrates of si and sll as the molar volumes of methane and propane hydrate, respectively. The molar volume of these hydrates, and therefore of the standard states, is well-characterized via diffraction data (Tse, 1990 Huo, 2002). Ballard proposed the following expression for the molar volume of water in hydrates ... 

The standard enthalpy of formation of a compound, AHf, is defined as the increment in enthalpy associated with the reaction of forming a given compound from its elements, with each substance in its thermodynamic standard state at the given temperature.2 The thermodynamic cycle for the enthalpy of formation of methane (CH4) from the standard states of carbon and hydrogen (graphite and hydrogen molecules) is shown in Figure 1. 

As an example let us consider the enthalpy change when methane is formed from its elements, both reactants and product being in their standard states. This is called the standard enthalpy of formation and written AH°. 

The standard state of each element is defined as the most stable form at 1 atm and the temperature specified (most frequently enthalpies of formation are measured and quoted at 298 K), The direct reaction cannot conveniently be carried out, but it is relatively easy to measure the enthalpy of combustion of methane in an apparatus called a flame calorimeter. As AH = q)p (Section 2.7), when methane is burnt with oxygen the heat produced gives the enthalpy of combustion directly,... 

The equilibrium partial pressure of methane for hydrate formation at 267 K is approximately 2.0 MPa, and at 255 K it is 1.5 MPa Using the fact that the standard states for this reaction are pure methane as a gas at 1 bar, and water and the hydrate as a pure solid ... 

In a formation equation, 1 mole of a compound forms from its elements. The standard heat of formation (AH ) is the enthalpy change for the formation equation when all the substances are in their standard states. For instance, the formation equation for methane (CH4) is... 

It does not matter that we cannot make this reaction occur cleanly and therefore cannot directly measure its enthalpy change. As seen above, indirect methods can be used. In such ways it is found that for this reaction is -17.9 kcal. Since we have arbitrarily taken the enthalpies of the reactants to be zero, it follows that on this basis the enthalpy of CH4 (g) is —17,9 kcal mol" h This is known as the enthalpy of formation, AHf, of methane. It.is important to use the term enthalpy of formation only for the formation of the compound from elements in their standard states. 

In this pathway for the combustion of methane, the reactants are first taken apart in reactions (a) and (b) to form the constituent elements in their standard states, which are then used to assemble the products in reactions (c) and (d). 

Such identical conditions in the formation of different compounds are called standard conditions. This is pressure 10 Pa = 1 bar. Before, the standard pressure was 1 atm = 1982 101.325 kPa. The same pure substance under such conditions may be in a different a regate state (gas, liquid, solid). In particular, compound H O may be in liquid and vapor states. That is why mean free enthalpy is evaluated as substance formation to its most stable state imder standard conditions, which is called standard state. For the compoimd H O such standard state is liquid, for methane -gaseous, for NaCl - solid. 

In 4.5.5 we computed residual properties for gaseous mixtures of methane and sulfur hexafluoride mixtures at 60°C and 20 bar. In 5.3.1 and 5.3.2 we computed excess properties for this same mixture. We can also compute residual properties for the ideal solution (Lewis-Randall standard state). Comparisons of these three kinds of difference measures are shown in Table 5.1 for equimolar mixtures. We see that the equimolar mixture of methane and sulfur hexafluoride exhibits positive deviations... 

So the calculated activity of dissolved methane is lO"". With a standard state of ideal 1 molal methane, this means WCH4TCH4 = 10 , and on the reasonable assumption that 7 4 = 1-0, then Wch4 = 10 . So in spite of the fact that two different standard states are used for the same component in the same reaction, we arrive at a useful answer. This is because the standard states used do not... 

To illustrate this, we can choose a completely different standard state for the gaseous methane and see what happens. Our new standard state is ideal gaseous methane at some pressure chosen at random, such as 978.4852 bar. First, we need A G° of methane in this new state. Because the gas is ideal, this is easy. From Equation (8.5), and because for an ideal gas, f = P,... 

Table 7.2 presents some thermodynamic data for the solution of methane in water and in nonaqueous solvents. The most outstanding feature is the relatively large negative entropy and enthalpy of solution in water. In all of the following theoretical developments, we refer to the values of zl5 °(II) and Zl// °(II) as the standard entropy and enthalpy of solution, respectively. The connecting relations to the more common standard states are given in Section 4.11. 

Thus, in the case at hand (Equation 1.4), the value of AH° is the amount of heat liberated on complete combustion of Imol of the hydrocarbon methane (CHt) when the reactants and products are in their standard states. 

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