Answer 4.3.1: Why we need extents of reaction equations

Problem:

The reaction between propane and hydrogen chloride to form propyl chloride and hydrogen is carried out in a continuous reactor. The product stream is analyzed and found to contain 27.45 mole% C3H7Cl, 27.45 mole % H2 and 14.6% HCl. The feed to the reactor contains only propane and hydrogen chloride. Calculate the fractional conversion of the limiting reactant and the percentage by which the other reactant is in excess. If the molar flow rate of the feed stream is 290 mol/s, what is the extent of reaction? (Give its numerical value and its units.)

Explanation:

Extents of reaction equations are almost always used when we are trying to find out information immediately surrounding a reactor. There are a few general rules about writing them that we should remember before we try to do it:

  • 1) We need to have balanced stoichiometric reactions before we can write them.
  • 2) We need to have a labelled flowsheet so we can know which variables to put in.
  • 3) We use the [in - out + generation - consumption = 0] equation for steady state problems (which we'll almost always have until later classes).
  • 4) We can write an extent of reaction for each product or reactant in our equations.

Let's look at an example before we have you write your extent of reaction equations. Let's do an example where we use the following reaction and schematic diagram:

H + CH3OH -> H2 + CH2OH

We'll make a little extent of reaction table so you can see what the equations would look like here:

overall equation: in - out + generation - consumption = 0
H balance: F1, H - F2, H - ξ = 0
CH3OH balance: F1, CH3OH - F2, CH3OH - ξ = 0
H2 balance: F1, H2 - F2, H2 + ξ = 0
CH2OH balance: F1, CH2OH - F2, CH2OH + ξ = 0

So you'll be able to do your extents of reaction equations, let's focus on a few details on this general example:

We wrote [in - out] terms for the general case for each reactant or product. We did this so we could plug numbers in in place of these variables as we solve for them. We could have plugged in zeroes in a few places because we know that two of the species are not in our feed to the reactor.

There is often confusion about how to write the ξ terms, but it's really easy after you've done a few of them. Just remember that the sign is determined by whether the species is being used up (-) or being generated (+) by the reaction. In this case, too, all of the stoichiometric coefficients were 1 so we don't have anything like [2ξ] in our equations. More examples will help too, as you start to write more extents of reaction equations.

Click on the button below to go to the next part when you're pretty sure you see the pattern on how to write the extents of reaction equations.



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