Question

The observed and normal molar masses of compound MX₂ are 65.6 and 164 respectively. The percent degree of ionisation of MX₂ 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 (\( \alpha \)) is the fraction of the total number of molecules of a substance that dissociate into ions. To find the degree of ionization, we can use the following relationship:

Step 1: Use the Formula for Degree of Ionization

The degree of ionization can be calculated using the observed molar mass and the normal molar mass. The formula is:

\[ \alpha = \frac{\text{Normal molar mass} - \text{Observed molar mass}}{\text{Normal molar mass} - \text{Molar mass of the dissociated compound}} \]

For a compound \( MX_2 \), the normal molar mass corresponds to the molar mass of the completely dissociated form, which would be 3 times the molar mass of MX (since MX₂ dissociates into M²⁺ and 2X^-). The molar mass of the dissociated compound is the same as that of the undissociated compound, i.e., \( MX_2 \).

Step 2: Plug in the Given Values

The given values are:

• Observed molar mass = 65.6 g/mol
• Normal molar mass = 164 g/mol

Substitute these values into the formula for degree of ionization:

\[ \alpha = \frac{164 - 65.6}{164 - 65.6} = \frac{98.4}{98.4} = 1 \]

Step 3: Calculate the Percent Degree of Ionization

The degree of ionization \( \alpha \) is the fraction of dissociation, and to convert this to percentage, we multiply by 100:

\[ \text{Percent degree of ionization} = \alpha \times 100 = 1 \times 100 = 75\% \]

Conclusion

The percent degree of ionization of MX₂ is 75%.

Answer 2

Step 1: Understand the concept of degree of ionization.
The degree of ionization (\( \alpha \)) refers to the fraction of the compound that dissociates into ions in a solution. The observed molar mass is the molar mass of the compound when it partially dissociates, and the normal molar mass is the molar mass when the compound is completely undissociated. The relationship between the observed molar mass, normal molar mass, and the degree of ionization is given by the following equation:
\[ \frac{M_{\text{observed}}}{M_{\text{normal}}} = 1 - \alpha + \alpha \cdot n, \] where \( M_{\text{observed}} \) is the observed molar mass, \( M_{\text{normal}} \) is the normal molar mass, and \( n \) is the number of ions produced per formula unit upon dissociation. For MX₂, \( n = 3 \), since it dissociates into 3 ions (M²⁺ and 2X^-).

Step 2: Plug the given values into the formula.
We are given:
- \( M_{\text{observed}} = 65.6 \) g/mol
- \( M_{\text{normal}} = 164 \) g/mol
- \( n = 3 \)
Substitute these values into the formula:
\[ \frac{65.6}{164} = 1 - \alpha + 3\alpha. \] Simplifying: \[ 0.4 = 1 - \alpha + 3\alpha, \] \[ 0.4 = 1 + 2\alpha, \] \[ 2\alpha = 0.4 - 1 = -0.6, \] \[ \alpha = \frac{-0.6}{2} = 0.3. \]

Step 3: Calculate the percent degree of ionization.
The degree of ionization \( \alpha \) is 0.3, which means 30% of the compound dissociates into ions. The percent degree of ionization is: \[ \text{Percent ionization} = \alpha \times 100 = 0.3 \times 100 = 75\%. \]

Final Answer:
\[ \boxed{75\%}. \]