A) Calculate the pH of a buffer system that is 0.06 M HNO2 and 0.160 M NaNO2
B) What is the pH after 2.00 M NaOH are added to 1.00 L of this buffer
I can do part A but I don't know how to part B
The easiest way is to work up an ICE chart as below. I like to work in millimoles. For the original buffer, if we have 1L of the original buffer, we will have the following millimoles of HNO2 and NaNO2.
mmoles HNO2 = 0.06M x 1000 mL = 60
mmoles NaNO2 = 0.160M x 1000 mL = 160
You don't say how much 2M NaOH is added to the buffer. I will use 1.0 mL of 2M = 2.0 mmoles.
..........HNO2 + OH^- ==> NO2^- + H2O
initial...60......0........160
added............2.0...........
change...-2.0....-2.0......+2.0
equil......58.....0.........162
Then pH = pKa + log(base)/(acid)
pH = pKa + log (162/58) = ??
By the way, the correct way is to work in M (and not millimoles) so that for (base) we substitute moles/L which will be 162 mmoles/1001 mL = ?? and for (acid) we substitute 58 mmoles/1001 mL. So the HH equation looks like this.
pH = pKa + log (162/1001)/(58/1001) BUT you notice that the 1001 denominator in each cancels so we are left with 162/58. After working a few thousand of these problems I think in terms of millimoles because I know the volume part will ALWAYS cancel. I mention this because some profs count off for using millimoles and not the "real" concn term. (I did in my classes.) I tried to get the students into the habit of writing
pH = pKa + log(162/V)/(58/V) and the Vs cancel no matter what V is. That way we don't need to do an extra division for the numerator and another division for the denominator before finding the fraction for mmols base/mmols acid.
To solve part B) of the question, you need to understand how the addition of a strong base, in this case NaOH, affects the pH of a buffer solution. When a strong base is added to a buffer system, it reacts with the weak acid component of the buffer.
Here are the steps to calculate the pH after NaOH is added to the buffer system:
1. Determine the reaction between the weak acid (HNO2) and the strong base (NaOH). The reaction is as follows:
HNO2 + NaOH -> NaNO2 + H2O
2. Calculate the amount of weak acid that reacts with the strong base. Since the ratio between weak acid and strong base in the buffer is 1:1, subtract the moles of NaOH added from the initial moles of HNO2:
moles of HNO2 remaining = initial moles of HNO2 - moles of NaOH added
For example, if 2.00 M NaOH is added to 1.00 L of the buffer solution, then the moles of HNO2 remaining can be calculated as follows:
moles of HNO2 remaining = (0.06 mol/L) - (2.00 mol/L * 1.00 L) = -1.94 mol
3. Consider the volume change due to the addition of NaOH. In this case, the volume remains constant at 1.00 L, so there is no need for any volume adjustments.
4. Calculate the new concentration of HNO2 in the buffer solution. Divide the moles of HNO2 remaining by the new volume of the buffer solution:
new concentration of HNO2 = moles of HNO2 remaining / new volume of buffer
For example, if the new volume is still 1.00 L, then:
new concentration of HNO2 = (-1.94 mol) / (1.00 L) = -1.94 M
Note: The negative concentration indicates an excess of the strong base and a conversion of the weak acid to its conjugate base.
5. Calculate the new concentration of NaNO2 in the buffer solution. Since the ratio between the weak acid and its conjugate base is 1:1, the new concentration of NaNO2 will be equal to the absolute value of the moles of HNO2 remaining:
new concentration of NaNO2 = |moles of HNO2 remaining| / new volume of buffer
For example:
new concentration of NaNO2 = |-1.94 mol| / (1.00 L) = 1.94 M
6. Calculate the pH of the buffer solution after the addition of NaOH. To do this, you can use the Henderson-Hasselbalch equation:
pH = pKa + log([NaNO2] / [HNO2])
- To find pKa, you need to know the Ka (acid dissociation constant) value for HNO2. Look up the Ka value in a reference source or use the ionization constant expression for HNO2: Ka = [H+][NO2-] / [HNO2].
- Plug the pKa value and the new concentrations of NaNO2 and HNO2 into the Henderson-Hasselbalch equation to calculate the pH.
Note: If the equation shows a negative logarithm (logarithm of a negative number), you may need to adjust the signs or convert the concentration values to logarithmic form (pM).
By following these steps, you should be able to calculate the pH of the buffer solution after adding NaOH.