A pilot plant discharges an acidic waste stream that must be neutralized and held at…

CHEMISTRY · Multi-part · A Level · Chemistry · Acids and bases · Acids and bases

Problem

A pilot plant discharges an acidic waste stream that must be neutralized and held at pH

7.20\pm0.10

before release. Because of environmental regulations, the ionic strength of the treated effluent cannot exceed

0.040\,\text{M}

. Three potential buffer systems are proposed and summarized below:

System	Weak Acid Formula	$K_a$ at $25\,^{\circ}\text{C}$	Activity Coefficient of Ions at $0.040\,\text{M}$ Ionic Strength
1	$\mathrm{H_{2}PO_{4}^{-}}/\mathrm{HPO_{4}^{2-}}$	$6.2\times10^{-8}$	$\gamma_{1-}=0.80$ , $\gamma_{2-}=0.77$
2	$\mathrm{HCOOH}/\mathrm{HCOO^{-}}$	$1.8\times10^{-4}$	$\gamma_{\text{neutral}}=1.00$ , $\gamma_{1-}=0.83$
3	$\mathrm{H_{2}CO_{3}}/\mathrm{HCO_{3}^{-}}$	$4.3\times10^{-7}$	$\gamma_{\text{neutral}}=1.00$ , $\gamma_{1-}=0.82$

For each charged species, the activity

a_i

is related to its concentration

[i]

a_i=\gamma_i[i]

. Assume that neutral species have

\gamma=1.00

. Temperature is constant at

25\,^{\circ}\text{C}

. The treatment tank holds

5.00\,\text{m}^3

of solution. (1) Part 1: (a) For each proposed buffer system, calculate the effective

pK_a

that accounts for the given ionic-strength-dependent activity coefficients. (2) Part 2: (b) Using your results from part (a), determine which buffer system best satisfies the discharge requirement of pH

7.20\pm0.10

. Provide quantitative justification. (3) Part 3: (c) For the buffer system chosen in part (b), compute the total moles of conjugate base and conjugate acid that must be added to the

5.00\,\text{m}^3

tank to achieve pH

7.20

, while ensuring that the combined molar concentration of charged species does not exceed the

0.040\,\text{M}

ionic-strength limit. Show all reasoning steps. (4) Part 4: (d) Suppose the waste stream flow rate suddenly doubles, introducing an additional

5.0\,\text{mol}

of strong acid per hour into the tank. Assuming perfect mixing and the buffer composition calculated in part (c), estimate the steady-state pH of the tank if no changes are made to the buffer feed. Clearly explain any approximations used.

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