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( 1.0 × 10 −4 ) ( 1.8 × 10 −6 ) = 9.8 × 10 −5 M

The concentration of NaOH is:

9.8 × 10 −5 M NaOH 0.101 L = 9.7 × 10 −4 M

The pOH of this solution is:

pOH = −log [ OH ] = −log ( 9.7 × 10 −4 ) = 3.01

The pH is:

pH = 14.00 pOH = 10.99

The pH changes from 4.74 to 10.99 in this unbuffered solution. This compares to the change of 4.74 to 4.75 that occurred when the same amount of NaOH was added to the buffered solution described in part (b).

Check your learning

Show that adding 1.0 mL of 0.10 M HCl changes the pH of 100 mL of a 1.8 × 10 −5 M HCl solution from 4.74 to 3.00.


Initial pH of 1.8 × 10 −5 M HCl; pH = −log[H 3 O + ] = −log[1.8 × 10 −5 ] = 4.74
Moles of H 3 O + in 100 mL 1.8 × 10 −5 M HCl; 1.8 × 10 −5 moles/L × 0.100 L = 1.8 × 10 −6
Moles of H 3 O + added by addition of 1.0 mL of 0.10 M HCl: 0.10 moles/L × 0.0010 L = 1.0 × 10 −4 moles; final pH after addition of 1.0 mL of 0.10 M HCl:

pH = −log [ H 3 O + ] = −log ( total moles H 3 O + total volume ) = −log ( 1.0 × 10 −4 mol + 1.8 × 10 −6 mol 101 mL ( 1 L 1000 mL ) ) = 3.00

If we add an acid or a base to a buffer that is a mixture of a weak base and its salt, the calculations of the changes in pH are analogous to those for a buffer mixture of a weak acid and its salt.

Buffer capacity

Buffer solutions do not have an unlimited capacity to keep the pH relatively constant ( [link] ). If we add so much base to a buffer that the weak acid is exhausted, no more buffering action toward the base is possible. On the other hand, if we add an excess of acid, the weak base would be exhausted, and no more buffering action toward any additional acid would be possible. In fact, we do not even need to exhaust all of the acid or base in a buffer to overwhelm it; its buffering action will diminish rapidly as a given component nears depletion.

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The indicator color (methyl orange) shows that a small amount of acid added to a buffered solution of pH 8 (beaker on the left) has little affect on the buffered system (middle beaker). However, a large amount of acid exhausts the buffering capacity of the solution and the pH changes dramatically (beaker on the right). (credit: modification of work by Mark Ott)

The buffer capacity    is the amount of acid or base that can be added to a given volume of a buffer solution before the pH changes significantly, usually by one unit. Buffer capacity depends on the amounts of the weak acid and its conjugate base that are in a buffer mixture. For example, 1 L of a solution that is 1.0 M in acetic acid and 1.0 M in sodium acetate has a greater buffer capacity than 1 L of a solution that is 0.10 M in acetic acid and 0.10 M in sodium acetate even though both solutions have the same pH. The first solution has more buffer capacity because it contains more acetic acid and acetate ion.

Selection of suitable buffer mixtures

There are two useful rules of thumb for selecting buffer mixtures:

  1. A good buffer mixture should have about equal concentrations of both of its components. A buffer solution has generally lost its usefulness when one component of the buffer pair is less than about 10% of the other. [link] shows an acetic acid-acetate ion buffer as base is added. The initial pH is 4.74. A change of 1 pH unit occurs when the acetic acid concentration is reduced to 11% of the acetate ion concentration.
    A graph is shown with a horizontal axis labeled “Added m L of 0.10 M N a O H” which has markings and vertical gridlines every 10 units from 0 to 110. The vertical axis is labeled “p H” and is marked every 1 unit beginning at 0 extending to 11. A break is shown in the vertical axis between 0 and 4. A red curve is drawn on the graph which increases gradually from the point (0, 4.8) up to about (100, 7) after which the graph has a vertical section up to about (100, 11). The curve is labeled [ C H subscript 3 C O subscript 2 H ] is 11 percent of [ C H subscript 3 CO subscript 2 superscript negative].
    The graph, an illustration of buffering action, shows change of pH as an increasing amount of a 0.10- M NaOH solution is added to 100 mL of a buffer solution in which, initially, [CH 3 CO 2 H] = 0.10 M and [ CH 3 CO 2 ] = 0.10 M .
  2. Weak acids and their salts are better as buffers for pHs less than 7; weak bases and their salts are better as buffers for pHs greater than 7.

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