When You Saw It, What Was
the Extent of Your Reaction? Part 3

DOFPro Team

When You Saw It, What Was
The Extent of Your Reaction?
Parts 1, 2, and 3

  • Address chemical reactors as modeled with extent of reaction and fractional conversion.
  • Moles are not conserved in chemical reactions.

Summary of Multiple Reactions

The problem statement was:

\(2.00\ \mathrm{kmol/s}\) of propane are burned in 25% excess oxygen in a faulty combustor. 100% of the hydrogen combusts to form water, but only 80% of the carbon combusts completely to \(\mathrm{CO_2}\). The remainder combusts to \(\mathrm{CO}\).

  1. Calculate the molar flow rate of oxygen into the combustor.
  2. Calculate the molar flow rates of each of the combustion products.
  3. Calculate the total molar flow rate of the exhaust.

Solution

Part a. \[ \dot{n}_\mathrm{O_2in} = 12.5\ \mathrm{kmol/s} \]

Part b.

\[ \dot{n}_\mathrm{CO_2out} = 4.8\ \mathrm{kmol/s}, \]

\[ \dot{n}_\mathrm{COout} = 1.2\ \mathrm{kmol/s} \]

\[ \dot{n}_\mathrm{O_2out} = 3.10\ \mathrm{kmol/s} \]

\[ \dot{n}_\mathrm{H_2Oout} = 8.00\ \mathrm{kmol/s} \]

Part c.

\[ \dot{n}_\mathrm{out} = 17.1\ \mathrm{kmol/s} \]

Yield and Selectivity

There are usually multiple reactions generating one desired product and one or more undesired products. We then define for desired species \(\mathrm{R}\),

Yield

\[ Y_\mathrm{R} = \frac{n_{\mathrm{R_{actual}}}}{n_{\mathrm{R_{possible}}}} \]

Selectivity

\[ S_\mathrm{R} = \frac{n_{\mathrm{R}}}{n_{\mathrm{products_{undesired}}}} \]

The goal is almost always high yield and high selectivity.

Yield Example

Assume that the desired product in the previous example was \(\mathrm{CO_2}\) and that the undesired product was \(\mathrm{CO}\).

If all of the propane were converted to \(\mathrm{CO_2}\), then

\[ \dot{n}_\mathrm{CO_2possible} = \frac{\nu_\mathrm{CO_2}}{-\nu_\mathrm{C_3H_8}}\dot{n}_\mathrm{C_3H_8in}=\frac{3}{-(-1)}2 = 6\ \mathrm{kmol/s} \]

\[ \dot{n}_\mathrm{CO_2actual} = \dot{n}_\mathrm{CO_2out} = 4.8\ \mathrm{kmol/s} \]

\[ Y_\mathrm{CO_2} = \frac{\dot{n}_\mathrm{CO_2actual}}{\dot{n}_\mathrm{CO_2actual} } = \frac{4.8}{6.0} = 0.80 = 80\% \]

Which we also could have gotten from the problem statement.

Selectivity Example

Assume that the desired product in the propane example was \(\mathrm{CO_2}\) and that the undesired product was \(\mathrm{CO}\).

\[ S_\mathrm{CO_2} = \frac{\dot{n}_\mathrm{CO_2out}}{\dot{n}_\mathrm{COout}} = \frac{4.8}{1.2} = 4 \]

We don’t count the water as an undesired product because it uses none of the \(\mathrm{C}\) in the propane, which is the only species that goes to our desired product.

If there had been other carbon containing compounds, e.g., \(\mathrm{CH_4}\), we would have included their flows in the denominator.

Mole Fraction, Split Fraction, and Fractional Conversion

It’s easy to get mole fraction, split fraction, and fractional conversion confused.

Mole Fraction
Also called composition, the moles of a species, such as \(\mathrm{A}\) divided by the total number of moles, \(x_\mathrm{A} = n_\mathrm{A}/(\sum n_i)\).
Split Fraction
The moles of a species, such as \(\mathrm{A}\), coming out of a separator in a given stream, such as stream 1, divided by the moles of \(\mathrm{A}\) going into a separator, \(t_{A1} = \dot{n}_\mathrm{A1}/\dot{n}_\mathrm{Ain}\).
Fractional Conversion
The moles of a reactant, such as \(\mathrm{A}\), converted to products in a reactor or process, \(f_\mathrm{A} = (\dot{n}_\mathrm{A_{in}} - \dot{n}_\mathrm{A_{out}})/\dot{n}_\mathrm{A_{in}} = 1 - (\dot{n}_\mathrm{A_{out}}/\dot{n}_\mathrm{A_{in}})\)

The Takeaways

  1. For reactors with multiple reactions occurring, there is often one desired reaction product and one or more undesired reaction product.
  2. The yield is the fraction of the desired product that could be produced that is actually produced..
  3. The selectivity is the ratio of the desired product to the undesired products.
  4. Don’t confuse mole fraction, \(x_\mathrm{A} = n_\mathrm{A}/(\sum n_i)\), split fraction, \(t_{A1} = \dot{n}_\mathrm{A1}/\dot{n}_\mathrm{Ain}\), and fractional conversion.\(f_\mathrm{A} = (\dot{n}_\mathrm{A_{in}} - \dot{n}_\mathrm{A_{out}})/\dot{n}_\mathrm{A_{in}}\).






Thanks for watching!
The Full Story companion video is in the link in the upper left. Recycling Before Recycling Was Cool, the next video in the series, is in the upper right. To learn more about Chemical and Thermal Processes, visit the website linked in the description.