Find and show work the final pH when 35mL of 0.200 mol/l sulfuric acid are titrated with 18mL of 0.030 mol/L sodium hydroxide?
To find the final pH when sulfuric acid is titrated with sodium hydroxide, we need to consider the stoichiometry of the reaction and the resulting concentrations of the species.
The balanced equation for the reaction between sulfuric acid (H2SO4) and sodium hydroxide (NaOH) is:
H2SO4 + 2NaOH -> Na2SO4 + 2H2O
From the equation, we can see that 1 mole of sulfuric acid reacts with 2 moles of sodium hydroxide.
Given:
Volume of sulfuric acid (H2SO4) = 35 mL = 0.035 L
Concentration of sulfuric acid (H2SO4) = 0.200 mol/l
Volume of sodium hydroxide (NaOH) = 18 mL = 0.018 L
Concentration of sodium hydroxide (NaOH) = 0.030 mol/L
First, let's calculate the moles of sulfuric acid and sodium hydroxide:
Moles of H2SO4 = Volume (in L) * Concentration
= 0.035 L * 0.200 mol/L
= 0.007 mol
Moles of NaOH = Volume (in L) * Concentration
= 0.018 L * 0.030 mol/L
= 0.00054 mol
Since the reaction between H2SO4 and NaOH is in a 1:2 ratio, the limiting reagent is sodium hydroxide (NaOH). This means that all of the sodium hydroxide will be used up in the reaction, and there will be some excess sulfuric acid left over.
To calculate the moles of remaining sulfuric acid, we subtract the moles of NaOH used from the initial moles of H2SO4:
Moles of H2SO4 remaining = Moles of H2SO4 initially - Moles of NaOH used
= 0.007 mol - 2 * 0.00054 mol
= 0.00692 mol
To calculate the concentration of sulfuric acid in the final solution, divide the moles of remaining sulfuric acid by the total volume (in liters) of the solution:
Concentration of H2SO4 = Moles of H2SO4 remaining / Total volume of solution (in L)
= 0.00692 mol / (0.035 L + 0.018 L)
= 0.129 mol/L
Now, we can calculate the pH using the formula:
pH = -log[H+]
In this case, since sulfuric acid (H2SO4) is a strong acid, it completely dissociates in water, resulting in a 1:1 ratio of H+ ions to sulfuric acid. Therefore, the concentration of H+ ions is equal to the concentration of sulfuric acid:
[H+] = Concentration of H2SO4
= 0.129 mol/L
Now, let's calculate the pH:
pH = -log(0.129)
= 0.89
Therefore, the final pH of the solution after the titration is 0.89.