Question

I need help finding the rate law, the relationship between rate and k, and lastly how to find max k.

Consider the following reaction which follows zero-order reaction kinetics

            2 A(g) + Catalyst(s) → B(g)              ΔH = -273.33 kJ

Notice that the reaction is exothermic, so in a closed system it is possible for this to get out of hand: The reaction releases energy, which increases the temperature, which increases the rate, which makes it heat up faster, which makes it react faster… this is a positive feedback loop that can become a thermal runaway hazard!

You will be using a constant-temperature bath as a heat sink to regulate the temperature and to remove excess energy from the system; however, let’s say the bath is only capable of removing up to 416.67 kJ of heat per minute. Given the information below, it is your task to determine the maximum temperature allowed before the rate of reaction creates a thermal runaway.

Assume a 1.00 L reaction tank.

Temperature, °C	k, M/s
25	0.001286
35	0.001984
45	0.002792
55	0.004109

Hints:

Start with the rate of heat removal from the bath, -416.67 kJ/min—this represents the maximum amount of heat that can be released by the reaction per minute before a thermal runaway occurs. You can use the enthalpy of the reaction to convert this into a proper rate: M/s

What is the rate law for this zero-order reaction and what is the relationship between rate and k?

I need step-by-step solutions, please...

I have that the rate of heat is 0.0508 M/s, now I am stuck trying to figure out how to determine max k.

Answer 1

Rate law for a zero order reaction is rate, r =k For the equation, 2 A(g) + Catalyst(s) – B(g) AH = -273.33 kJ Amount of heat removed per minute = 416.67 kJ/minute heat released per mole = -273.33 kJ heat released for 2 moles of A 273.33 T deg C 25 35 45 k, M/S 0.001286 0.001984 0.002792 0.004109 heat released per sec (kJ/s) heat released per minute (kJ/min) 0.35 21.09 0.54 32.54 0.76 45.79 1.12 67.39 kmax, M/s 0.025407017 6.94 416.67 Therefore kmax when the reaction becomes runaway reaction is 0.0254 M/s

PLEASES