Stream enthalpies for the DME process (uakron, 7min) can be estimated using the "heat of reaction" pathway (Fig 3.5a) or the "heat of formation" pathway (Fig 3.5b). This presentation is based on Fig 3.5b, which is very similar to Fig 2.6c. The main difference is the inclusion of the heat of formation for each compound relative to its elements. Including the heat of formation puts the reference state for each compound on the same basis of comparison (ie. the elements). If one stream (e.g. "products") possesses more enthalpy than another stream (e.g. "reactants") then the energy difference between the streams (e.g. "heat of reaction") would be accounted for by simply subtracting the two stream enthalpies. Reactions inherently involve multiple components, so including the heats of formation in the stream enthalpies, as well as the other enthalpic contributions represented in Fig 2.6c, is inevitable. These sample calculations are illustrated for all the streams appearing in the DME process. The presentation follows up on the discussion of Fig 2.6c for pure fluids. Once you understand the calculations for each pure fluid, the mixture property simply involves taking the molar average, so: H ≈ ∑(x_{i}*Hf_{i}+Cp_{i}^{ig}ΔT+(q_{i}-1)*H_{i}^{vap}). In this equation, (q_{i}-1)*H_{i}^{vap }accounts crudely for departures from ideal gas behavior. For example, if a stream is a vapor, then q=1 and H^{vap }doesn't matter. If q=0, then the stream is a liquid and H^{vap }must be subtracted. We will study more accurate models of ideal gas departures in Unit II.

Comprehension Questions:

1. Compute the enthalpy, H(J/mol), of methanol at 250C and 2 bars relative to its ideal gas standard state elements.

2. Compute the enthalpy, H(J/mol), of DME at 250C and 2 bars relative to its ideal gas standard state elements.

3. Compute the enthalpy, H(J/mol), of water at 250C and 2 bars relative to its ideal gas standard state elements.

4. Compute the enthalpy, H(J/mol), of a stream that is 50% methanol, 25% DME, and 25% water at 250C and 2 bars relative to its ideal gas standard state elements.

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## Stream Enthalpy Using the "Heat of Formation" Pathway

Stream enthalpies for the DME process (uakron, 7min) can be estimated using the "heat of reaction" pathway (Fig 3.5a) or the "heat of formation" pathway (Fig 3.5b). This presentation is based on Fig 3.5b, which is very similar to Fig 2.6c. The main difference is the inclusion of the heat of formation for each compound relative to its elements. Including the heat of formation puts the reference state for each compound on the same basis of comparison (ie. the elements). If one stream (e.g. "products") possesses more enthalpy than another stream (e.g. "reactants") then the energy difference between the streams (e.g. "heat of reaction") would be accounted for by simply subtracting the two stream enthalpies. Reactions inherently involve multiple components, so including the heats of formation in the stream enthalpies, as well as the other enthalpic contributions represented in Fig 2.6c, is inevitable. These sample calculations are illustrated for all the streams appearing in the DME process. The presentation follows up on the discussion of Fig 2.6c for pure fluids. Once you understand the calculations for each pure fluid, the mixture property simply involves taking the molar average, so:

H≈ ∑(x*_{i}Hf+_{i}CpΔ_{i}^{ig}T+(q-1)*_{i}H). In this equation, (_{i}^{vap}q-1)*_{i}Haccounts crudely for departures from ideal gas behavior. For example, if a stream is a vapor, then_{i}^{vap }q=1 andHdoesn't matter. If^{vap }q=0, then the stream is a liquid andHmust be subtracted. We will study more accurate models of ideal gas departures in Unit II.^{vap }Comprehension Questions:

1. Compute the enthalpy, H(J/mol), of methanol at 250C and 2 bars relative to its ideal gas standard state elements.

2. Compute the enthalpy, H(J/mol), of DME at 250C and 2 bars relative to its ideal gas standard state elements.

3. Compute the enthalpy, H(J/mol), of water at 250C and 2 bars relative to its ideal gas standard state elements.

4. Compute the enthalpy, H(J/mol), of a stream that is 50% methanol, 25% DME, and 25% water at 250C and 2 bars relative to its ideal gas standard state elements.