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pset06_soln

# pset06_soln - HOMEWORK 6 KEY Problem 1 Quoting from the...

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Unformatted text preview: HOMEWORK 6 KEY Problem 1 : Quoting from the Wilmington, DE Morning News , Aug. 3, 1977: “Investigators sift through the debris from blast in quest for the cause [why the new chemical plant exploded]. A company spokesman said it appears… likely that the [fatal] blast was caused by [rapid decomposition of] … ammonium nitrate [NH 4 NO 3 ] used to produce nitrous oxide [N 2 O].” In the process, a T=200 o F aqueous solution, 83 wt% ammonium nitrate, is fed into a CSTR. When the process is running normally at steady state, about 140 kg/hr of the aqueous solution is injected, and the temperature in the reactor, T R , is 510 o F. At this temperature, the water evaporates rapidly, but the molten ammonium nitrate remains in the CSTR, slowly decomposing by this reaction: NH 4 NO 3 (liquid) Æ N 2 O(g) + 2 H 2 O(g) k(T=510 o F) = 0.307/hour ∆ H rxn (T=510 o F) = -740 kJ/kg of ammonium nitrate Note that it takes about 2.2 MJ to convert a kg of liquid water at 200 o F to a kg of steam at 500 o F. Also, FYI: Cp(steam) = 2 kJ/kg-degree F Cp(liquid NH 4 NO 3 ) = 0.8 kJ/kg-degree F Neglect non-ideal mixing effects and assume that NH 4 NO 3 enters as a liquid. Assume that ∆ H rxn is approximately constant in the reactor temperature ranges of the problem. A diagram is shown below. Cite as: William Green, Jr., and K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. gaseous products at T R liquid feed, including water and ammonium nitrate at 200 o F Pure liquid ammonium nitrate at T R CSTR This document will follow these symbolic conventions when multiple interpretations are possible: An extensive property is given by an underbar A molar intensive property has no extra notational information An intensive property that is per unit of mass is given with a carrot Extents of reaction are in units of moles per time Also, ideal mixing is assumed. (a) During normal steady-state operation, what mass (kg) of ammonium nitrate resides in the reactor? Note that there is negligible hold-up of any gases within the reactor. Input state: liquid water and liquid ammonium nitrate are fed at 200 o F Reaction State: temperature is T R , negligible gases are present Output state: only gases may exit, gases exit at T R The components are renamed A, B, and C as in the following: A(l) => B(g) + 2C(g) A = ammonium nitrate B = N 2 O C = H 2 O First, define extent of reaction ξ & in terms of reaction rate: Cite as: William Green, Jr., and K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. ξ & = rV = k [ A ] V = kN A = ( k / MW A )( N A MW A ) = ( k / MW A )( m A ) Mole/mass balances on each component in the system yield the following relationships: Ammonium Nitrate Balance...
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pset06_soln - HOMEWORK 6 KEY Problem 1 Quoting from the...

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