Question

How many moles of sodium hypobromite (NaBrO) must be added to a 2.00 L solution of 0.025 M hypobromous acid (HBrO) to form a buffer solution of pH 9.0 (Ka HBrO is 2.5x10^-9)? Assume the volume of solution does not change on addition of NaBrO?

a) How many moles of sodium hypobromite (NaBrO) must be added to a
2.00 L solution of 0.025 M hypobromous acid (HBrO) to form a buffer solution of pH
9.0 (Ka HBrO is 2.5x10^-9)? Assume the volume of solution does not change on
addition of NaBrO?

b) If you started with a solution of 0.500 M HBrO and made a pH 9.0
buffer, would the buffer capacity of this system be larger, smaller or the same as the
one in part A. Explain in no more than 3 sentences.

Answer 1

(a)

0.125 mol

(b)

Larger. See below

Explanation:

(a)

Hypobromous acid is a weak acid and dissociates:

`sf(HBrOrightleftharpoonsH^(+)+OBr^(-))`

For which:

`sf(K_a=([H^+][OBr^(-)])/([HOBr])=2.5xx10^(-9)color(white)(x)"mol/l"" "color(red)((1)))`

Please note that these refer to equilibrium concentrations and not initial concentrations.

The initial number of moles of `sf(HOBr)` is given by:

`sf(n_(HOBr)=cxxv=0.025xx2=0.050)`

Since `sf(pH=9)` then `sf([H^+]=10^(-pH)=10^(-9)color(white)(x)"mol/l")`

Rearranging `sf(color(red)((1))` gives:

`sf([H^(+)]=K_axx([HBrO])/([BrO^(-)])" "color(red)((2))`

At this point I will make the important assumption that, because the value of `sf(K_a)` is so small, then the equilibrium concentrations are a good approximation to the initial concentrations.

The fact that you are asked to assume that the volume change is negligible is actually irrelevant. Since `sf([color(white)(x)]=n/v)` you can see that the volume is common to both acid and co - base so will cancel in `sf(color(red)((2))`.

This means we can write out `sf(color(red)((2))` using moles`sf(rArr`

`:.` `sf(10^(-9)=2.5xx10^(-9)xx(0.050)/(nBrO^(-))`

`:.` `sf(nBrO^(-)=(2.5xxcancel(10^(-9))xx0.050)/(cancel(10^(-9)))=0.125)`

(b)

From `sf(color(red)((2))` you can see that the pH of the buffer depends on the ratio of acid to co - base concentrations, whereas the amount of added `sf(H^+)` or `sf(OH^-` which the buffer can cope with will depend on the individual concentrations of acid and co - base.

This is referred to as the buffer capacity.

In (b) to maintain a pH of 9 the concentration of `sf(HOBr)` and of `sf(OBr^(-))` must have both been increased, so we would expect a greater buffer capacity.