# Units

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*[m

^{3}/s],

*v*[m/s], and

*A*[m

^{2}]?

*f*=

*Av,*that is

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 O_{2}) = 0.4 kg O_{2}

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