Equimolar solutions of the following compounds are prepared separately in water. Which will have the lowest pH value?

We are given equimolar solutions of BeCl$$_2$$, SrCl$$_2$$, CaCl$$_2$$, and MgCl$$_2$$. We need to determine which solution has the lowest pH. Since pH measures acidity, the solution that is most acidic will have the lowest pH.

All these compounds are chlorides of alkaline earth metals. When dissolved in water, they dissociate into their respective cations and anions:

For BeCl$$_2$$: BeCl$$_2$$ → Be$$^{2+}$$ + 2Cl$$^-$$

For MgCl$$_2$$: MgCl$$_2$$ → Mg$$^{2+}$$ + 2Cl$$^-$$

For CaCl$$_2$$: CaCl$$_2$$ → Ca$$^{2+}$$ + 2Cl$$^-$$

For SrCl$$_2$$: SrCl$$_2$$ → Sr$$^{2+}$$ + 2Cl$$^-$$

The chloride ion (Cl$$^-$$) is the conjugate base of a strong acid (HCl), so it does not hydrolyze and does not affect the pH. Therefore, the acidity of the solution depends on the hydrolysis of the metal cations (M$$^{2+}$$).

The hydrolysis reaction for a divalent metal cation is:

M$$^{2+}$$ + H$$_2$$O ⇌ M(OH)$$^+$$ + H$$^+$$

This reaction produces H$$^+$$ ions, which lower the pH. The extent of hydrolysis depends on the charge density of the cation. Charge density is the ratio of charge to ionic radius. Since all cations have a +2 charge, charge density is inversely proportional to ionic radius. A higher charge density means the cation can polarize the O-H bond in water more effectively, facilitating the release of H$$^+$$ ions and making the solution more acidic.

Now, compare the ionic radii of the cations:

• Be$$^{2+}$$ has the smallest ionic radius because beryllium is in period 2.
• Mg$$^{2+}$$ has a larger radius than Be$$^{2+}$$ (period 3).
• Ca$$^{2+}$$ has a larger radius than Mg$$^{2+}$$ (period 4).
• Sr$$^{2+}$$ has the largest radius among these (period 5).

The order of ionic radii is: Be$$^{2+}$$ < Mg$$^{2+}$$ < Ca$$^{2+}$$ < Sr$$^{2+}$$.

Therefore, the charge density order is: Be$$^{2+}$$ > Mg$$^{2+}$$ > Ca$$^{2+}$$ > Sr$$^{2+}$$.

This means Be$$^{2+}$$ has the highest charge density and will hydrolyze the most, producing the highest concentration of H$$^+$$ ions, resulting in the lowest pH.

Additionally, due to its small size and high charge density, beryllium compounds exhibit more covalent character, further enhancing hydrolysis and acidity in water.

Hence, among the given options, BeCl$$_2$$ solution will be the most acidic and have the lowest pH.

The options are:

A. BeCl$$_2$$

B. SrCl$$_2$$

C. CaCl$$_2$$

D. MgCl$$_2$$

So, the correct answer is Option A.