Question

The observed and normal molar masses of compound MX\(_2\) are 65.6 and 164 respectively. The percent degree of ionisation of MX\(_2\) is \(\_\_\_\_\)% (Nearest integer).
 

Hint:

The degree of ionization can be determined by comparing the observed molar mass with the normal molar mass. For a compound that dissociates into multiple ions, consider the ionic molar mass as the molar mass after complete dissociation.

Answer 1

The degree of ionization (\(\alpha\)) can be found using the relation between the observed molar mass and normal molar mass of the compound. The normal molar mass (\(M_{normal}\)) is the molar mass of the compound if it were completely ionized, and the observed molar mass (\(M_{observed}\)) is the molar mass in the solution. The degree of ionization \(\alpha\) is given by: \[ \alpha = \frac{M_{normal} - M_{observed}}{M_{normal} - M_{ionic}} \] where \(M_{ionic}\) is the molar mass of the ionized compound. Here, we are given: \[ M_{normal} = 164, \quad M_{observed} = 65.6 \] Since MX\(_2\) dissociates into 3 ions (MX\(_2\) → M\(^+\) + 2X\(^-\)), the molar mass of the ionic form would be: \[ M_{ionic} = \frac{M_{normal}}{3} = \frac{164}{3} = 54.67 \] Now, we can calculate the degree of ionization: \[ \alpha = \frac{164 - 65.6}{164 - 54.67} = \frac{98.4}{109.33} \approx 0.9 \] To express this as a percentage: \[ \alpha \times 100 = 90\% \] Thus, the degree of ionization of MX\(_2\) is approximately \(40\%\).