Q18 P - Chemistry: Molecular Nature Of Matter And Change

Question

Boyle’s law relates gas volume to pressure, and Avogadro’s law relates gas volume to number of moles. State a relationship between gas pressure and number of moles.

Step-by-Step Solution

Answer

At constant temperature and volume, the pressure of the gas is directly proportional to the number of moles of the gas.

Step 1: Boyle’s law and Avogadro’s law

Boyle’s law: According to Boyle’s law, “the volume of the gas changes according to its pressure at constant temperature”. It means that, at constant temperature, the volume of the gas is inversely proportional to its pressure.

$$\begin{gathered} V \alpha \frac{1}{P} \\ PV=cons\tan t(T,n fixed) \end{gathered}$$

Where, V = volume, T = temperature, P = pressure, n = number of moles

Charles’s Law: According to Avogadro’s law, “at constant temperature and pressure, the number of moles of gas is directly proportional to the volume”.

$$\begin{gathered} V \alpha n \\ \frac{V}{n}=cons\tan t (P,T fixed) \end{gathered}$$

Step 2: Relationship between pressure and number of moles

Combining both laws,

According to Boyle’s law,

$\begin{array}{rcl}PV& =& cons\tan t (T,n fixed)\\ V& =& \frac{cons\tan t}{P}\end{array}$

Put above value in the Avogadro’s law,

$$\begin{gathered} \frac{V}{n}=cons\tan t(Avogadro\text{'}s law) \\ \frac{{\displaystyle \frac{cons\tan t}{P}}}{n}=cons\tan t\Rightarrow \frac{P}{n}=cons\tan t\Rightarrow P \alpha n \end{gathered}$$

Thus, at constant temperature and volume, the pressure of the gas is directly proportional to the number of moles of the gas.