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.

1 Answer
Sep 21, 2016

Answer:

(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.