$2\mathrm{.}11.$ In the mid$-$nineteenth century the entomologist Henri Fabre noted that French ants $($garden variety$)$ busily bustled about their business on hot

Problems

$35$

days but were rather sluggish on cool days. Checking his results with Oregon ants, I find

Running speed,$\frac{m}{h}r,150,160,230,295,370$

Temperature, $C,13,16,22,24,28$

What activation energy represents this change in bustliness?

$2\mathrm{.}12.$ The maximum allowable temperature for a reactor is $800K.$ At present our operating set point is $780K,$ the $20-K$ margin of safety to account for fluctuating feed, sluggish controls, etc. Now, with a more sophisticated control system we would be able to raise our set point to $792K$ with the same margin of safety that we now have. By how much can the reaction rate, hence, production rate, be raised by this change if the reaction taking place in the reactor has an activation energy of $175k\frac{J}{m}ol?$

$2\mathrm{.}13.$ Every May $22$ I plant one watermelon seed. I water it$,$ I fight slugs, I pray, I watch my beauty grow, and finally the day comes when the melon ripens. I then harvest and feast. Of course, some years are sad, like $1980,$ when a bluejay flew off with the seed. Anyway, six summers were a pure joy and for these I've tabulated the number of growing days versus the mean daytime temperature during the growing season. Does the temperature affect the growth rate? If so$,$ represent this by an activation energy.

$\backslash$table$[[$Year$,1976,1977,1982,1984,1985,1988],[$Growing days,$87,85,74,78,90,84],[$Mean temp, $C,22\mathrm{.}0,23\mathrm{.}4,26\mathrm{.}3,24\mathrm{.}3,21\mathrm{.}1,22\mathrm{.}7]]$

$2\mathrm{.}14.$ On typical summer days, field crickets nibble, jump, and chirp now and then. But at a night when great numbers congregate, chirping seems to become a serious business and tends to be in unison. In $1897,$ A$.$ E$.$ Dolbear $($Am$.$ Naturalist, $31,970)$ reported that this social chirping rate was dependent on the temperature as given by

$(numberof$ chirps $in15s)+40=($ temperature, $F)$

Assuming that the chirping rate is a direct measure of the metabolic rate, find the activation energy in $k\frac{J}{m}ol$ of these crickets in the temperature range $60-80F.$

$2\mathrm{.}15.$ On doubling the concentration of reactant, the rate of reaction triples. Find the reaction order.

For the stoichiometry $A+B($products$)$ find the reaction orders with respect to A and $B.$