How many moles of NaOH would you need to add to 800 ml of a 0.4 M H2CO3
solution in order to bring the pH of the solution to 10.5?
To answer this question, we need to understand the concept of pH and how it relates to the concentration of hydrogen ions (H+) in a solution. pH is a logarithmic scale that indicates the acidity or alkalinity of a solution, with values below 7 being acidic, 7 being neutral, and above 7 being alkaline or basic.
In this case, we need to add NaOH (sodium hydroxide) to a solution of 0.4 M H2CO3 (carbonic acid) to increase the pH from an initial value to 10.5. Carbonic acid is a weak acid that can partially dissociate in water according to the following equation:
H2CO3 ⇌ H+ + HCO3-
The addition of NaOH will react with the hydrogen ions (H+) from the carbonic acid and form water, thus increasing the pH. The reaction can be represented as follows:
NaOH + H+ → Na+ + H2O
To determine the amount of NaOH needed, we can use the balanced equation and the concept of stoichiometry. The balanced equation tells us that for every mole of NaOH, one mole of H+ reacts. Therefore, the amount of NaOH needed will be equal to the amount of H+ ions present in the solution.
First, let's calculate the initial amount of H+ ions in the solution using the given concentration and volume:
Molarity (M) = moles of solute / liters of solution
Given: Molarity (H2CO3) = 0.4 M
Volume = 800 ml = 800/1000 liters = 0.8 liters
Using the given molarity and volume:
Moles of H2CO3 = Molarity × Volume = 0.4 M × 0.8 L = 0.32 moles
Since H2CO3 dissociates into one H+ ion and one HCO3- ion, the initial amount of H+ ions is also 0.32 moles.
Now let's calculate the amount of NaOH needed to reach a pH of 10.5. To do this, we need to calculate the difference in the concentration of H+ ions between the initial pH and the desired pH.
pH = -log[H+]
To convert pH to [H+], we use the following equation:
[H+] = 10^(-pH)
Initial [H+] = 10^(-pH_initial) = 10^(-10.5)
Desired [H+] = 10^(-pH_desired) = 10^(-10.5)
Now, subtract the desired [H+] from the initial [H+] to find the difference:
Difference in [H+] = Initial [H+] - Desired [H+]
The difference in [H+] will represent the amount of H+ ions that need to be neutralized by NaOH.
Finally, since the balanced equation tells us that one mole of NaOH reacts with one mole of H+, the amount of NaOH needed will be equal to the difference in [H+] calculated above.
To summarize, to find the number of moles of NaOH needed to bring the pH of the solution to 10.5:
1. Calculate the initial amount of H+ ions using the molarity and volume of the H2CO3 solution.
2. Convert the initial and desired pH values to [H+] concentrations.
3. Find the difference in [H+].
4. The amount of NaOH needed will be equal to the difference in [H+] calculated above.