Question

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Answer 1

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):

`\begin{gathered} P* V=n* R* T \\ R=(P* V)/(n* T) \end{gathered}`

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:

`R=\frac{(atm)*(L)}{(\text{mol)}*(K)}`

Thus, R should be obtained in atm.L/mol.K