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# Heat of Reaction How do I know which is the "correct" way to write the reaction?

We need to calculate the heat produced by a set of $$N_R$$$$\mathrm{N_R}$$ reactions in our reactor model.

\begin{align} Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j} \end{align}\begin{align} \mathrm{Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j}} \end{align}

$$Rr_j$$$$\mathrm{Rr_j}$$ is the reaction rate of reaction $$j$$$$\mathrm{j}$$, in $$\frac{kmol}{kg_{cat} s}$$$$\mathrm{\frac{kmol}{kg_{cat} s}}$$

$$\Delta H_{R,j}$$$$\mathrm{\Delta H_{R,j}}$$, in $$\frac{kJ}{kmol}$$$$\mathrm{\frac{kJ}{kmol}}$$, is constant and calculated as:

\begin{align} \Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f \end{align}\begin{align} \mathrm{\Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f} \end{align}

Now consider these: \begin{align} R1: \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align}\begin{align} \mathrm{R1:}\ \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} R2: \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}\begin{align} \mathrm{R2:}\ \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\Delta H_R$$$$\mathrm{\Delta H_R}$$ that is twice the $$\Delta H_R$$$$\mathrm{\Delta H_R}$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?

# Heat of Reaction

We need to calculate the heat produced by a set of $$N_R$$ reactions in our reactor model.

\begin{align} Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j} \end{align}

$$Rr_j$$ is the reaction rate of reaction $$j$$, in $$\frac{kmol}{kg_{cat} s}$$

$$\Delta H_{R,j}$$, in $$\frac{kJ}{kmol}$$, is constant and calculated as:

\begin{align} \Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f \end{align}

Now consider these: \begin{align} R1: \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} R2: \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\Delta H_R$$ that is twice the $$\Delta H_R$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?

# How do I know which is the "correct" way to write the reaction?

We need to calculate the heat produced by a set of $$\mathrm{N_R}$$ reactions in our reactor model.

\begin{align} \mathrm{Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j}} \end{align}

$$\mathrm{Rr_j}$$ is the reaction rate of reaction $$\mathrm{j}$$, in $$\mathrm{\frac{kmol}{kg_{cat} s}}$$

$$\mathrm{\Delta H_{R,j}}$$, in $$\mathrm{\frac{kJ}{kmol}}$$, is constant and calculated as:

\begin{align} \mathrm{\Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f} \end{align}

Now consider these: \begin{align} \mathrm{R1:}\ \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} \mathrm{R2:}\ \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\mathrm{\Delta H_R}$$ that is twice the $$\mathrm{\Delta H_R}$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?

2 added 3 characters in body

We need to calculate the heat produced by a set of $$N_R$$ reactions in our reactor model.

\begin{align} Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j} \end{align}

$$Rr_j$$ is the reaction rate of reaction $$j$$, in $$\frac{kmol}{kgcat s}$$$$\frac{kmol}{kg_{cat} s}$$

$$\Delta H_{R,j}$$, in $$\frac{kJ}{kmol}$$, is constant and calculated as:

\begin{align} \Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f \end{align}

Now consider these: \begin{align} R1: \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} R2: \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\Delta H_R$$ that is twice the $$\Delta H_R$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?

We need to calculate the heat produced by a set of $$N_R$$ reactions in our reactor model.

\begin{align} Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j} \end{align}

$$Rr_j$$ is the reaction rate of reaction $$j$$, in $$\frac{kmol}{kgcat s}$$

$$\Delta H_{R,j}$$, in $$\frac{kJ}{kmol}$$, is constant and calculated as:

\begin{align} \Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f \end{align}

Now consider these: \begin{align} R1: \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} R2: \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\Delta H_R$$ that is twice the $$\Delta H_R$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?

We need to calculate the heat produced by a set of $$N_R$$ reactions in our reactor model.

\begin{align} Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j} \end{align}

$$Rr_j$$ is the reaction rate of reaction $$j$$, in $$\frac{kmol}{kg_{cat} s}$$

$$\Delta H_{R,j}$$, in $$\frac{kJ}{kmol}$$, is constant and calculated as:

\begin{align} \Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f \end{align}

Now consider these: \begin{align} R1: \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} R2: \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\Delta H_R$$ that is twice the $$\Delta H_R$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?

1

# Heat of Reaction

We need to calculate the heat produced by a set of $$N_R$$ reactions in our reactor model.

\begin{align} Q_r = \sum_{j=1}^{Nr} Rr_j*\Delta H_{R,j} \end{align}

$$Rr_j$$ is the reaction rate of reaction $$j$$, in $$\frac{kmol}{kgcat s}$$

$$\Delta H_{R,j}$$, in $$\frac{kJ}{kmol}$$, is constant and calculated as:

\begin{align} \Delta H_{R,j} = \sum_{i=1}^{Nc}\nu_{i,j}*\Delta h_{i,j}^f \end{align}

Now consider these: \begin{align} R1: \ce{H2 + 1/2O2 \rightarrow H_2O} \end{align} \begin{align} R2: \ce{2H2 + O2 \rightarrow 2H_2O} \end{align}

They are undoubtedly the same reaction, but the R2 gives a $$\Delta H_R$$ that is twice the $$\Delta H_R$$ in R1. It is naturally so, but greatly affects my energy balance.

How do I know which is the "correct" way to write the reaction?

Does it mean that the reaction rate should be specific to R1 or R2?