Explain how to prepare 1L of a buffer at pH 7.4 using 1M hypochlorous acid (Ka = 3.5 x 10-8) and a 1 M NaOH solution. Indicate the volume of hypochlorous acid and sodium hydroxide to use.
To prepare a 1L buffer solution at pH 7.4 using 1M hypochlorous acid (Ka = 3.5 x 10^-8) and a 1M NaOH solution, we need to calculate the amounts of hypochlorous acid and sodium hydroxide required.
A buffer solution is made up of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, hypochlorous acid (HOCl) acts as a weak acid, and its conjugate base, hypochlorite ion (OCl-), is formed when it accepts a hydroxide ion (OH-) from sodium hydroxide (NaOH).
The Henderson-Hasselbalch equation is used to calculate the pH of a buffer:
pH = pKa + log ([A-]/[HA])
Here, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. In this case, the weak acid is hypochlorous acid, and the conjugate base is hypochlorite ion.
Given that the desired pH is 7.4, we can set up the equation as follows:
7.4 = pKa + log ([OCl-]/[HOCl])
Since the concentration of the base ([OCl-]) is unknown and the concentration of the acid ([HOCl]) is given as 1M, we need to solve for the concentration of the base using the Henderson-Hasselbalch equation.
Rearranging the equation, we get:
log ([OCl-]/[HOCl]) = 7.4 - pKa
log ([OCl-]/1) = 7.4 - (3.5 x 10^-8)
Now, we can calculate the concentration of the base:
[OCl-]/1 = 10^(7.4 - (3.5 x 10^-8))
[OCl-] = 10^(7.4 - (3.5 x 10^-8))
Now that we know the concentration of the conjugate base ([OCl-]), we can calculate the volume of hypochlorous acid (1M) and sodium hydroxide (1M) needed to prepare a 1L buffer solution.
To calculate the volume of hypochlorous acid, we can use the following formula:
Volume of hypochlorous acid (L) = (concentration of hypochlorous acid (M) * volume of the buffer solution (L)) / concentration of the hypochlorous acid (M)
Plugging in the values:
Volume of hypochlorous acid (L) = (1M * 1L) / 1M
Volume of hypochlorous acid (L) = 1L
Therefore, you need to use 1 liter (L) of 1M hypochlorous acid.
To calculate the volume of sodium hydroxide, we can use the same formula:
Volume of sodium hydroxide (L) = (concentration of sodium hydroxide (M) * volume of the buffer solution (L)) / concentration of the hypochlorite ion (M)
Plugging in the values:
Volume of sodium hydroxide (L) = (1M * 1L) / [OCl-]
Remember that [OCl-] was calculated earlier. Compute [OCl-] from the previous equation and substitute it in the above equation to get the volume of sodium hydroxide required.
By following these calculations, you can prepare a 1L buffer solution at pH 7.4 using 1M hypochlorous acid and a 1M NaOH solution.