Dissolving Barium Hydroxide in Water: Calculating the Vapor Pressure of the Solution

In this article, we will explore the process of dissolving barium hydroxide (text{Ba(OH)}_2) in water and calculating the resulting vapor pressure of the saturated solution. The vapor pressure of pure water at 25°C is 23.8 mmHg. We will use Raoult's Law to predict the vapor pressure of a solution containing barium hydroxide.

Introduction to Barium Hydroxide Dissolution

Barium hydroxide, text{Ba(OH)}_2, is a strong base that dissociates in aqueous solutions. Understanding the dissociation behavior is critical to predicting the vapor pressure of its saturated solutions.

Dissociation of Barium Hydroxide in Water

Barium hydroxide dissociates in water according to the following equation:

text{Ba(OH)}_2(aq) → text{Ba}^{2 }(aq) 2text{OH}^--(aq)

From this dissociation, it is clear that 1 mole of text{Ba(OH)}_2 produces 3 moles of ions in the solution: 1 mole of text{Ba}^{2 } and 2 moles of text{OH}^-.

Concentration of the Saturated Solution

The solubility of text{Ba(OH)}_2 at 25°C is approximately 0.1 mol/L. This means that in 1 liter of solution, 0.1 moles of text{Ba(OH)}_2 will dissolve to produce 3 moles of ions.

To calculate the total concentration of ions in a saturated solution:

Total moles of ions 3 × 0.1 mol/L 0.3 mol/L

Calculate the Mole Fraction of Water

To determine the mole fraction of water, we need to find the number of moles of water in the solution. The density of water is approximately 1 g/mL, so in 1 liter (1000 mL), there are 1000 grams of water.

Moles of water 1000 g / 18 g/mol ≈ 55.56 mol

The total moles in the solution are:

Total moles 55.56 0.1 55.66 mol

The mole fraction of water, (X_{text{H}_2text{O}}), is then calculated as:

(X_{text{H}_2text{O}} frac{55.56}{55.66} ≈ 0.997)

Apply Raoult's Law

Using Raoult's Law, the vapor pressure of the water in the solution can be calculated. Raoult's Law states:

(P_{text{solution}} X_{text{H}_2text{O}} × P^_{circ}{text{H}_2text{O}})

(P_{circ}{text{H}_2text{O}} 23.8 mmHg)

Substituting the values:

(P_{text{solution}} 0.997 × 23.8 mmHg ≈ 23.7 mmHg)

Conclusion

The vapor pressure of a saturated solution of text{Ba(OH)}_2 at 25°C is approximately 23.7 mmHg.