(10 Points) A water initially contains 50 mg/L of Mg

2+
The pH of the water is increased .
until the concentration of hydroxide ion is 0.0005 M. Calculate the concentration (mg/L)
of magnesium ion in this water at this pH. Assume that the temperature of the solution
is 25˚C

To calculate the concentration of magnesium ion in the water, we need to understand the chemical reactions that occur when the pH is increased and hydroxide ions are formed.

When water is ionized, it dissociates partially into H+ (hydrogen ions) and OH- (hydroxide ions). At 25°C, the self-ionization constant of water (Kw) is 1.0 x 10^-14.

H2O ⇌ H+ + OH-

By increasing the pH, we are adding an alkaline substance, such as sodium hydroxide (NaOH), which dissociates in water to produce hydroxide ions (OH-). The reaction can be represented as:

NaOH → Na+ + OH-

The hydroxide ions (OH-) combine with the magnesium ions (Mg2+) already present in the water to form the insoluble compound magnesium hydroxide (Mg(OH)2):

Mg2+ + 2OH- → Mg(OH)2

Since the concentration of hydroxide ions (OH-) is given as 0.0005 M, we can calculate the concentration of magnesium ion (Mg2+) in the water.

First, we need to convert the concentration of hydroxide ions to moles per liter (mol/L). Given that the concentration of hydroxide ions is 0.0005 M, we have:

0.0005 mol/L OH-

The stoichiometric ratio of hydroxide ions to magnesium ion is 2:1. Therefore, the concentration of magnesium ion is half the concentration of hydroxide ions:

0.0005 mol/L OH- --> 0.00025 mol/L Mg2+

To convert the concentration of magnesium ion from moles per liter (mol/L) to milligrams per liter (mg/L), we need to consider the molar mass of magnesium (24.31 g/mol) and the valence charge of magnesium ion (2+).

0.00025 mol/L Mg2+ * 2 (valence charge of Mg2+) * 24.31 g/mol Mg * 1000 mg/g = X mg/L

Calculating this expression gives us the concentration of magnesium ion in milligrams per liter (mg/L) in the water at the given pH when the concentration of hydroxide ions is 0.0005 M.

Please perform the calculation using the given values to obtain the final answer.