Question

Happy Diwali to all..
What is the difference between max and minimum value of pH of Buffer solution.
How to calculate the difference.​

Answer 1

Answer:

by taking the negative log of the concentration of hydrogen ions and measuring the maximum and minimum value and then finding the difference would be a great idea

Answer 2

Answer:

Explanation:

The buffer solution is most effective when it does not let addition of small amount of base change the value of pH. This happens when the buffer capacity is maximum.

According to Henderson-Hasselbalch equation,

pH=pKa+log[Salt]/[Acid]for a buffer solution.

Let [salt] = a, [acid] = b

Hence, pH=pKa+log(a/b)

When, x molar base is added to the solution, the equation becomes,

pH=pKa+log(a+x)/(b−x)…….[i]

Now, Buffer capacity(β) is defined as,

β=x/Δ(pH)

Therefore, βit can be written as,

β=dx/d(pH)

Using value of pH from [i],

β=dx/d(pKa+log(a+x)/(b−x))

i.e. β=1/(d(pKa+log(a+x)/(b−x))/dx)

On differentiating, we get,

β=2.303/((b−x)((b−x)+(a+x))/(a+x)(b−x)2)

On simplifying,

β=2.303(a+x)(b−x)/(a+b)

i.e. β=2.303(−x2+(b−a)x+ab)/(a+b)

Now, for maximum buffer capacity, we need to find the maxima of β.

For that, dβ/dx=0

i.e. dβ/dx=2.303(−2x+(b−a))/(a+b)=0

thus, −2x+(b−a)=0

Which gives us, x=(b−a)/2…..[ii]

For checking when the buffer is most effective without adding base, put x=0 in [ii],

We get, a=b

This tells us that when no base is added to the solution, buffer is most effective i.e. buffer capacity is maximum when a=b or [salt] = [acid]

Putting [salt] = [acid] in the Henderson-Hasselbalch equation,

pH=pKa+log1

Hence, pH=pKa