Question

(25 pts) Solve for the time-dependent concentration of ammonium chloride based on the following reaction equation. Assume that the reaction rate constants and the concentrations of ammonia and hydrogen chloride are constant. Assume an initial concentration of ammonium chloride of 0.5mM. Be sure to solve for the constants. NH3+HCl NH4CI Reaction: a. (5 pts) Write the reaction rate equation for NH2C b. (5 pts) Write the differential equation in our standard form (+A -y = B) dx c. (5 pts) Determine the integration factor (IF) for this equation d. (10 pts) Solve the differential equation to determine the ammonium chloride concentration as a function of time. Solve for your integration constant using the initial conditions.

Answer 1

1. Here the reaction is assumed to be of zeroth order because there is no dependence of rate of concentration of reactants as the concentration of reactants are constant,

2. The differential equation is a linear one. Hence it is solved by evaluating the corresponding Integrating factor.

3. Constant of integration is evaluated by applying initial condition at t=0, c=0.

Date / Given : NH3 + HClNHACI A + B C Assume reaction rate constand and concentration of Nrz & He to be constant (Given) TA = RCA oCo 1 Cao & CBO are unitial conc. of A & B respectively (mol) a-rate constant (m3.s ) mol het r=kCAO CBO = ki where k' is zeroth orde rate constant (mol ) (mas) Her reaction is considered Ho be cloth or dee because there is no dependency g rate of reaction on a cono of reactante so a relative rates of oxn re=k -RA -8B = r. part

no NHACI entes reactor so, NHACS in . Date: overall oglance on NHACI I NHACI Treffe tt Nres, a generated ? - moi) NHACI accumulated - mol Hell NHACI is considered as product c VoC +Vkl = vde & is conc . of NHACI in (mol m3 dc dt +-k = o C part B dc + roc = at v o where a =V 2 space time (s) et/2 part c TIF =

Date: 1 Solving differential can ho constant cett - rketle dt + x of centegrat - Cet/2 = ket/2x2 + x cetle = ka ette tal Now use to find & an untial Lets make condition of At the start of the process reaction only has reactants A & B but no c so at t=0, C=0 o. e .k2 + x => 11-1=kz Sub ③ in ① c et/a a kaetla - R2 et/2 v patt dividing Te = kr(1-entre)