RMP Lecture Notes

Choosing a Basis

Early in the solution of most balance problems, you must choose a "basis of calculation." The basis is a reference you choose for the calculations you plan to make.

Your basis is a fixed number -- all other values are determined relative to it.

EXAMPLE:
Basis

What is the mole fraction of ethylene in the product?

In the above example, any value of F0 could be used to determine the answer. You may very well have decided to pick a value so that you could use numbers instead of symbols.

In this problem, the value you choose for F₀ is your basis of calculation. In many problems, you can make the arithmetic easier by choosing a good basis. In the example, there are at least three "obvious" choices.

Some of these have "easier" numbers than others, and so would be better choices.

Just as we always began thermo problems by declaring the system, it is good practice to write down your basis at the beginning of any material balance problem.

Your basis can be a period of time, a given mass of material, or a flow rate. Often, you can see a good basis in a problem statement -- but as you get good at this, you will learn when the given numbers are not a good choice.

When a weight analysis of solids or liquids are given, it is often most convenient to choose 1 or 100 lbs or kg as your basis. For gases 1 or 100 moles is useful (especially if the gas is ideal).

EXAMPLE:
Himmelblau Exmpl 1.13 Aromatic hydrocarbons form 15-30% of the components of leaded fuels and as much as 40% of unleaded gasoline. The carbon to hydrogen ratio helps to characterize the fuel components. If a fuel is 80% C and 20% H by weight, what is the C/H ratio in moles?

If a basis of 100 lb (or kg) of fuel is selected, then % = lbs.

You could have chosen any number in mass units -- say 7 kg -- as your basis, but it would have made the problem arithmetic a little less friendly.

EXAMPLE: Himmelblau Example 1.14 Given that a 50.0 lb test run of gas averages 10.0 mol % H2, 40.0 % CH4, 30.0% CO, and 20.0% CO2, what is the average molecular weight?

You might choose your basis to be 50.0 lbs -- it is given. But note that the composition is in mole percent. It would probably be more convenient to choose a basis to take advantage of the composition data - - you can always scale it to the 50 lbs later (if necessary).

You can solve a problem on one basis, then shift it to get your final answer. (What if the example above had asked how much CO was in a 60.0 lb run? You could work the problem with a basis of 100 mols to calculate the molecular weight, then use that to determine the moles in 60.0 lbs, the composition to find the CO, and its molecular weight to get an answer. And it would all be easier than trying to start with 50.0 lbs!).

References:

Felder, R.M. and R.W. Rousseau, Elementary Principles of Chemical Processes, 2nd Edition, John Wiley, 1986, pp. pp. 96-102.
Felder, R.M. and R.W. Rousseau, Elementary Principles of Chemical Processes, 2005 3rd Edition, 2005, p. 93-96.
Himmelblau, D.M., Basic Principles and Calculations in Chemical Engineering, 3rd Edition, Prentice-Hall, 1974, pp. 20- 22.

R.M. Price
Original: 6/9/94
Modified: 9/6/96, 9/10/98; 12/25/2004