100mL of dilute (5wt% ) aqueous solution of sodium alginate (Mw=216g/mol ), is introduced all at once as drops into a 500mL dilute aqueous solution of 1MHCl, producing spherical gels of uniform size of 2mm diameter. The sodium ions (Na+)in the droplets are ion-exchanged with the hydrogen ions (H) in the liquid, thereby producing soft gels of alginic acid. The mixture is agitated sufficiently well and the concentration of Na in the I/k of the liquid is uniform. The liquid is sampled at various times and the concentration of Na+is analysed using an atomic absorption instrument. Table Q1 and Figure Q1 below show the temporal profile' of Na+concentration in the liquid. Figure Q1 Temporal variation of Na+concentration in the liquid (a) Analyse the mass transfer process for this situation by assuming there is abundant Na ions at the interface between the droplets and the liquid in the vessel at short times, such that the concentration of Na+at the surface of the droplets is invariant with time. Develop a model of temporal variation of concentration of Na+in the liquid by making simplifying assumptions and show that: C1Ct=1eAkct/V where Ct is the concentration of Na ions in the liquid at time t,Cl is the concentration of Na+at the interface between the droplets and the liquid, A is the total interfacial area of the droplets, V is the volume of HCl solution, and K6 is the external film mass transfer coefficient. State your assumptions clearly. [10 marks] (b) Considering the temporal profile of Na+ion concentration in Figure Q1 and its dependence on kc, given by the above equation, show that k is given by: kc=ACimV where m is the slope of the tangent to the concentration curve at t=0. [2 marks] (c) Calculate the concentration of Na+in the droplets. [1 mark] (d) Show that the total surface area of the droplets, A, is 0.3m2. [2 marks] (e) Calculate the numerical value of kc in units of ms1. [5 marks]