Chapter MH, Problem 13PP

Solution

Interpretation: Whether the given equation is dimensionally correct or not needs to be determined.

Concept Introduction: Dimensional analysis: Whether any equation is dimensionally correct or not can be easily identified by studying the relation between the physical quantities using their dimensions and units. This is known as dimensional analysis. It helps in performing calculations as it keeps units the same. For any equation to be dimensionally correct, it doesn't have to be true.

No.

The given equation is as follows:

  $R=\frac{nT}{PV}$

Here, R is the gas constant, n is the number of moles, T is temperature, P is pressure and V is volume. The unit for n is mol, T is K, P is atm, V is L and R is $\text{L}·\text{atm/mol}·\text{K}$ .

Substituting the units and checking the RHS and LHS of the equation.

  $\begin{array}{l}R=\frac{nT}{PV}\\ \text{L atm/mol K}=\frac{\text{mol K}}{\text{atm L}}\end{array}$

Here, the equation is not dimensionally correct. Since the volume of pressure is atm and that of volume is L, the units will be satisfied only if PV is in the numerator and nT in the denominator.

The dimensionally correct equation will be:

  $R=\frac{pV}{nT}$

Thus, the given equation is not dimensionally correct.

For any equation to be dimensionally correct, the units must be the same on both sides of the equation.