Calculating the Mass of Barium Hydroxide Required for a Solution with pH 11

Barium hydroxide, Ba(OH)2, is a soluble basic compound widely used in several chemical applications, including as a buffer and in the laboratory. This article explains the steps necessary to calculate the required mass of barium hydroxide to prepare a 500 mL solution with a pH of 11.

A Step-by-Step Guide to Calculate the Mass of Barium Hydroxide

To find the mass of barium hydroxide needed to prepare a solution with a pH of 11, follow these steps:

Step 1: Determine the Concentration of Hydroxide Ions

The pH is related to the concentration of hydrogen ions by the equation: pH pOH 14. Given that the pH is 11, we can find the concentration of hydroxide ions

[OH-] 10-pOH 10-3 M

Step 2: Relate Hydroxide Concentration to Barium Hydroxide Concentration

Barium hydroxide dissociates in water as follows:

Ba(OH)2 → Ba2 2OH-

From this dissociation, we see that one mole of Ba(OH)2 produces two moles of OH-. Therefore, the concentration of barium hydroxide needed to achieve a hydroxide concentration of 10-3 M is:

[Ba(OH)2] [OH-] / 2 (10-3) / 2 5 × 10-4 M

Step 3: Calculate the Amount of Barium Hydroxide Required

To find the number of moles of Ba(OH)2 needed for 500 mL (0.5 L) of solution:

Moles of Ba(OH)2 [Ba(OH)2] × Volume (L) (5 × 10-4 M) × 0.5 L 2.5 × 10-4 moles

Step 4: Convert Moles to Mass

Now we need to convert moles of Ba(OH)2 to grams. The molar mass of Ba(OH)2 can be calculated as follows:

Barium (Ba): 137.33 g/mol Oxygen (O): 16.00 g/mol (2 O atoms) Hydrogen (H): 1.01 g/mol (2 H atoms)

Calculating the molar mass:

Molar mass of Ba(OH)2 137.33 (16.00 × 2) (1.01 × 2) 137.33 32.00 2.02 171.35 g/mol

Now we can find the mass:

mass moles × molar mass (2.5 × 10-4 moles) × 171.35 g/mol ≈ 0.042 g

Conclusion

To prepare a 500 mL solution with a pH of 11, you need approximately 0.042 grams of barium hydroxide (Ba(OH)2). This calculation can be verified using two methods, both of which lead to the same result: approximately 0.0428 grams of Ba(OH)2.

Additional Information

Understanding the dissociation and behavior of barium hydroxide in aqueous solutions can help in various applications, from chemical synthesis to practical laboratory uses. Knowing how to calculate the required mass is crucial for accurate preparation of solutions.