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A widely held belief is that unit analysis is the least interesting activity of the physical sciences. Indeed, carefully carrying units through a difficult formula is sometimes about as interesting as painting a barn. But there are several good reasons to pay attention to units.
You can lose valuable points if you drop units, substitute into a formula, and forget to convert cm to m or the like. One way to guard against this type of error is to automatically convert any number to MKS (meters, kilograms, and seconds) as you read the passage, or at least flag the units that are nonstandard (i.e., not meters, kilograms, and seconds). Another way is to keep track of the units any time the units in the problem are nonstandard.
Another reason to pay attention to units is that they can alert you if you have written an equation the wrong way.
For example, you may remember that flow rate f is the volume (m3) flowing past a point per unit time (s) and that it is related to the velocity v and cross-sectional area A of the pipe. But how do you relate f [m3/s], v [m/s], and A [m2]?
The only way to correctly obtain the units is to write something like
f = Av, that is
where we may have left out a proportionality constant. In this case the formula is correct as written. Units may bring back to mind an equation you would have forgotten, counting for valuable points.
A third reason for keeping track of units is that they sometimes guide you to an answer without your having to use a formula or do much work, as the next example shows.



How much volume does 0.4 kg of oxygen gas take up at T = 27° C and P = 12 atm? (Use the gas constant R = 0.0821 L atm/K mol.


Well, to the question, “How much oxygen?”, we can answer either in kilograms or in liters.
The problem gives kilograms and asks for liters, so this is a complicated units conversion problem.
We will essentially construct the ideal gas equation using the units of the elements in the problem.
We start with 0.4 kg.


(amount of O2) = 0.4 kg O2


In order to apply the ideal gas equation we need to convert to moles. We can do this by including the factors:




Both are equivalent to 1, but the units cancel, leaving us with moles.




Now we include a factor of R because it has liters in the numerator and moles in the denominator.
We obtain




This leaves us with units of atm and K which we want to get rid of.
In order to cancel them, we can just put them in.
This may seem strange, but it works. (Recall 27° C = 300 K.) Thus we obtain




For MCAT problems we generally work to one digit of accuracy, so we replace 0.0821 with 0.08, so that we have




It is generally safe to round to one significant digit. If it happens that two choices are close, then you can always go back and gain more accuracy.
This example involved more arithmetic than most MCAT problems, but its purpose was to point out that attention to units can speed up the solution to a problem. If this is the way you normally do such a problem, good. Most readers, however, would take longer working through this type of problem, using up valuable seconds on the MCAT. Remember that seconds can add up to points.

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