The question requires us to provide the definition of "dimensional analysis".
Dimentional analysis, also called unit-factor method, is the study of the relation between physical quantities based on their units. We can use it to find the unit that a constant should be expressed, for example, or to convert one unit to another.
Let's consider the following example of dimensional analysis: we know the units used for pressure (P), volume (V), temperature (T) and number of moles (n) of a system, and want to find out the unit that the constant of gases (R) should be written considering these quantities.
We know the units for the following quantities:
P --> atm
V --> L
T --> K
n --> mol
Considering the equation for ideal gases, we can rearrange it to find the constant of gases (R):
[tex]\begin{gathered} P\times V=n\times R\times T \\ R=\frac{P\times V}{n\times T} \end{gathered}[/tex]
Now, using the known units for pressure, volume, temperature and number of moles, we can find out the unit that should be used for the constant of gases:
[tex]R=\frac{(atm)\times(L)}{(\text{mol)}\times(K)}[/tex]
Thus, R should be obtained in atm.L/mol.K
