Final Answer:
The pH of the solution formed by dissolving 0.65 g of sodium hydroxide (NaOH) pellets in 5.0 L of water is approximately 13.0.
Step-by-step explanation:
Sodium hydroxide (NaOH) is a strong base that dissociates completely in water to produce hydroxide ions (OH⁻) and sodium ions (Na⁺). The dissociation reaction of NaOH can be represented as:
NaOH (s) → Na⁺ (aq) + OH⁻ (aq)
Given that 0.65 g of NaOH is dissolved in 5.0 L of water, we first need to calculate the molarity of the NaOH solution:
Molarity (M) = moles of solute / volume of solution in liters
To find the number of moles of NaOH, we use its molar mass:
Molar mass of NaOH = 22.99 g/mol (Na) + 15.999 g/mol (O) + 1.008 g/mol (H) = 39.997 g/mol ≈ 40 g/mol
Number of moles = Mass / Molar mass
Number of moles = 0.65 g / 40 g/mol ≈ 0.01625 mol
Now, plug the values into the formula for molarity:
Molarity = 0.01625 mol / 5.0 L = 0.00325 M
Since NaOH completely dissociates in water, the concentration of hydroxide ions (OH⁻) in the solution is also 0.00325 M. The pH of a solution can be calculated using the equation:
pOH = -log[OH⁻]
pOH = -log(0.00325) ≈ 2.49
pH + pOH = 14 (at 25°C)
pH ≈ 14 - 2.49 ≈ 13.0
Therefore, the pH of the NaOH solution is approximately 13.0, indicating a highly basic solution due to the presence of a significant amount of hydroxide ions.