Answer 4.3.1: Why we may or may not need to choose a basis in this problem

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:

There are normally a few clues in a problem statement that indicate that we are going to choose a basis (assume a flowrate somewhere in our solution). These are:

  • You aren't given any flowrates for any of the streams, or
  • You are asked to find answers that are numbers divided by each other, like answers that are percentages or answers that are fractions (i.e., fractional conversion).

In this problem, we are not given any flowrates until near the end of the problem statement when we are told that the feed is 290 mol/s and asked to find the extent of reaction when this flowrate is used. Our other two answers that we are asked to find fulfill the requirements in the list above since we are asked to find percent excess and fractional conversion. Both of these numbers are ratios so we might be able to choose a basis to find them. Then we could use a technique we've used before to find the extent of reaction when the feed is 290 mol/s.

If we are going to choose a basis somewhere, there are a few major details we should remember:

  • Never, ever, ever, use a flowrate given in the problem statement if you have assumed a flowrate anywhere in your solution.
    • There are some special cases where we can use scaling if this happens, though. (In fact, that's what we're going to do in this problem. We're going to choose a basis for our solution and solve as much as we can. Then we'll incorporate the 290 mol/s that is given later on.)
  • If you assume a basis somewhere, you can't decide to choose a basis anywhere else later on in your problem solution. You can only choose one!

So, you can only choose one flowrate to use in your problem solution if you are going to choose one.

We will solve this problem by choosing a basis flowrate for one of the streams. Which stream would you choose to assume a value for:

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