Final answer:
To calculate the pH of the diluted solution, determine the concentration of hydroxide ions by using the equation c1v1 = c2v2. From there, calculate the pOH using the equation pOH = -log[OH-] and then find the pH using the equation pH + pOH = 14.
Step-by-step explanation:
To calculate the pH of the diluted solution, we need to find the concentration of hydroxide ions (OH-) first. Since sodium hydroxide is a strong base, it completely ionizes in water, so the concentration of OH- ions is equal to the concentration of the sodium hydroxide solution. The initial concentration is given as 0.707 mol/L, and the volume is 0.135 L. By diluting the solution to a volume of 0.629 L, the concentration of OH- ions remains the same, but the volume increases. Using the equation c1v1 = c2v2, we can calculate the new concentration:
c1 = 0.707 mol/L, v1 = 0.135 L, v2 = 0.629 L
c2 = (c1v1) / v2 = (0.707 mol/L x 0.135 L) / 0.629 L = 0.152 mol/L
To find the pH, we need to calculate the pOH. The pOH is calculated using the equation pOH = -log[OH-]. Therefore, pOH = -log(0.152) = 0.818. Finally, we can find the pH using the equation pH + pOH = 14. Thus, pH = 14 - 0.818 = 13.182.