Question

Six litres of 0.4M 3-(N-morpholino) propane sulfonic acid (MOPS) buffer of pH 7.8 are required. Available in the laboratory are 10M HCl and 10M NaOH and the zwitterionic form of MOPS (M.Wt = 210.3). The pKa for the MOPS zwitter ion is 7.2. Describe, showing the relevant calculations, the procedure for preparing the buffer . If 10ml of 10M HCl was added to 1 litre of the above buffer (question 9) what would be the resulting pH?
What would be the resulting pH if 10ml of 10M HCl were added to 1 litre of pure water?

Answer 1

The following formula is used to calculate the pH of the given buffer

$pH=pK_a +lg(\dfrac{C_{BA}}{C_{HA}})$

$pK_a=7.2$

Rearranging the formula

$\dfrac{C_{BA}}{C_{HA}}=10^{{pH}-pK_a}\newline$

$=10^{7.8-7.2}=3.98$

The concentration of the buffer solution is $= 0.4M$

$C_{BA}+C_{HA}=0.4$

The concentration of MOPS and Na-salt required can be now evaluated

$3.98C_{HA}+C_{HA}=0.4\newline C_{HA}=\dfrac{0.4}{3.98+1}=0.08M$

$C_{BA}=0.4-0.08=0.32M$

Calculate the number of moles of HA and BA

$n(BA)=C_{BA}*V_{solution}\newline 0.32*6=1.92mol$

$n(HA)=C_{HA}*V_{solution}\newline 0.08*6=0.48mol$

The total number of moles of the solution is

$1.92+0.48=2.40mol$

Mass of MOPS=$2.4*210.3=504.7g$

Volume of NaOH=1.92/10=0.192 L

Mix 504.7 g of MOPS with 0.192 L of 10M NaOH solution

$C_7H_{15}NO_4S\ +NaOH\ =C_7H_{14}NO_4SNa\ +H_2O$

In a flask, dissolve this mixture with distilled water up to 6L after the reaction is complete

$pH=Pk_A +log(\dfrac{B}{A})$

$=7.2+log(0.32/0.08)\newline =7.2+log4\newline=7.8$