How to calculate Delta pH and Total Buffer Range

Question

We were doing a lab in biology which included testing how basic and acidic different liquid substances were, andwe would add different amounts of drops of NCI and NaOH liquid to see how good of a buffer it was. I have the data but it wants me to find the  Delta pH and Total Buffer Range,  and I cannot find the instructions anywhere on how to do this. Here's what I have for Tap Water, I'll try my best to type one of them  out since I can't seem to find an option to send/paste photos on this. Thanks in advance for the help.


Tap Water
Zero drops
Acid at 9.25
Basic 7.0

5 drops
Acid 3.35

Basic 11.4

 

10 drops
Acid 7.2

Basic 11.63

15 drops
Acid 3.1

Base 11.11

 

20 drops
Acid 3.0

Base 11.85

 

25 drops
Acid 2.9

Base 11.95

How do I calculate the ΔpH and Total Buffer Range from this data?

Answer 1

To calculate ΔpH and the Total Buffer Range, follow these steps:

1. Understanding the Terms:

1. ΔpH (Delta pH): This is the change in pH observed when the liquid is subjected to an acidic or basic solution. Calculate this by subtracting the initial pH (0 drops) from the pH after adding drops. ΔpH=Final pH−Initial pH (Zero drops)\Delta pH = \text{Final pH} - \text{Initial pH (Zero drops)}ΔpH=Final pH−Initial pH (Zero drops)
2. Total Buffer Range: This represents the range of pH over which the solution acts as a buffer. It's the difference between the lowest pH (with acid added) and the highest pH (with base added).

2. Steps to Calculate:

(a) Calculate ΔpH for Acid and Base Additions:

1. For each number of drops, subtract the pH at zero drops from the pH for that condition.

For Acid:

ΔpH (Acid)=pH (Acid at X drops)−pH (Acid at Zero drops)\Delta \text{pH (Acid)} = \text{pH (Acid at X drops)} - \text{pH (Acid at Zero drops)}ΔpH (Acid)=pH (Acid at X drops)−pH (Acid at Zero drops)

For Base:

ΔpH (Base)=pH (Base at X drops)−pH (Base at Zero drops)\Delta \text{pH (Base)} = \text{pH (Base at X drops)} - \text{pH (Base at Zero drops)}ΔpH (Base)=pH (Base at X drops)−pH (Base at Zero drops)

(b) Find the Total Buffer Range:

The Total Buffer Range is the difference between the lowest observed pH (with acid added) and the highest observed pH (with base added):

Total Buffer Range=Max pH (Base)−Min pH (Acid)\text{Total Buffer Range} = \text{Max pH (Base)} - \text{Min pH (Acid)}Total Buffer Range=Max pH (Base)−Min pH (Acid)

3. Example Calculation for Tap Water:

ΔpH Calculations:

For 5 drops:

1. Acid: ΔpH (Acid)=3.35−9.25=−5.90\Delta \text{pH (Acid)} = 3.35 - 9.25 = -5.90ΔpH (Acid)=3.35−9.25=−5.90
2. Base: ΔpH (Base)=11.4−7.0=4.40\Delta \text{pH (Base)} = 11.4 - 7.0 = 4.40ΔpH (Base)=11.4−7.0=4.40

Similarly, calculate for 10, 15, 20, and 25 drops.

Total Buffer Range:

1. Lowest pH (Acid): 2.9 (at 25 drops)
2. Highest pH (Base): 11.95 (at 25 drops)

Total Buffer Range=11.95−2.9=9.05\text{Total Buffer Range} = 11.95 - 2.9 = 9.05Total Buffer Range=11.95−2.9=9.05