September 14, 20XX
It all began when Professor Mori and Professor Siger summoned me, Diddy Kong, Toad, Tails, and Roll Light to their laboratory deep within the Mushroom Kingdom. The excitement in the air was palpable, for we were about to embark on a mission to create upgraded tools and gadgets for Mario the Plumber, Sonic the Hedgehog, and their allies.
As we gathered in the laboratory, Professor Mori and Professor Siger greeted us with enthusiasm. Their brilliant minds were already brimming with ideas for enhancing the abilities of our iconic heroes. It was clear that this collaboration would be a meeting of some of the brightest minds from various worlds.
The first order of business was to discuss the specific needs of Mario, Sonic, and their friends. Mario's list included an upgraded Super Mushroom that could provide him with even more power, an enhanced Fire Flower that could shoot larger fireballs, and a more versatile Super Star power-up. Sonic sought an advanced version of his Speed Shoes, a new and improved Electric Shield, and a gadget that could help him navigate underwater more efficiently.
Toad and Tails immediately started brainstorming ideas, scribbling diagrams, and calculating the necessary modifications. Roll Light, with her remarkable engineering skills, began crafting prototypes for the proposed upgrades. Professor Mori and Professor Siger provided invaluable guidance, offering insights into the scientific principles behind our ideas.
One of our most exciting breakthroughs came when Tails showed his expertise to me by creating a Super Mushroom that not only increased Mario's size and strength but also granted him temporary flight capabilities. They dubbed it the "Super Skyshroom." Mario was ecstatic when he tested it and soared through the Mushroom Kingdom skies at certain calculated distance.
Meanwhile, Roll Light designed a sleek and compact Power Sneaker for Sonic, which allowed him to maintain even greater speed and agility. It was equipped with energy-efficient thrusters and an automatic braking system. Sonic practically zoomed through the lab with joy during his trial run. To aid Sonic underwater, we devised a state-of-the-art Aqua Bubbler that created an air bubble around him, allowing him to breathe freely while submerged. This gadget also had an underwater propulsion system, making Sonic the fastest swimmer in the ocean.
The final piece of our collaborative effort was an Electric Forcefield for them individually. It could absorb and store electrical energy, enhancing his defensive capabilities. Professor Siger and Professor Mori perfected its design, ensuring it would work seamlessly with certain movements.
After hours of meticulous work and testing, we presented the upgraded tools and gadgets to Mario, Sonic, and their allies. Their excitement and gratitude were overwhelming. They promised to use these new enhancements to continue protecting their worlds from evil forces and to keep thrilling themselves with their heroic adventures.
Chem Notes: (filled with academic musings)
Zero Order: Rate = k[A]n
• If a reaction is zero order, the rate of the reaction does not change as concentration is changed.
• Doubling [A] will have no effect on the reaction rate.
• Rate law: Rate = k[A]0 = k
• Rate constant (k) units: Rate = M/sec, k = M/sec (M sec–1)
Zero Order: Rate = k
rate = k[NH3]0 = k
2 NH3(g) N2(g) + 3 H2(g)
First Order: Rate = k[A]n
• If a reaction is first order, the rate is directly proportional to the reactant concentration.
• Doubling [A] will double the rate of the reaction.
• Rate law: Rate = k[A]1 or Rate = k[A]
• Rate constant (k) units: When Rate = M/sec, k = sec–1
Second Order: Rate = k[A]n
• If a reaction is second order, the rate is directly proportional to the square of the reactant concentration.
• Doubling [A] will quadruple the rate of the reaction.
• Rate law: Rate = k[A]2
• Rate constant (k):
When Rate = M/sec, k = M−1 · sec−1
Finding the Rate Law: The Initial
Rate Method
• The rate law must be determined experimentally
• See how the the initial concentration of a reactant will affect the initial rate of the reaction.
• By changing the initial concentration of one reactant at a time, the effect of each reactant's concentration on the rate can be determined.
• In examining results, differences in reaction rate are compared that differ only in the concentration of one reactant.
Consider the reaction between nitrogen dioxide and carbon monoxide:
NO2(g) + CO(g) NO(g) + CO2(g)
The initial rate of the reaction is measured at several different concentrations of the reactants with the results shown at right. From the data, determine:
a. the rate law for the reaction
b. the rate constant (k) for the reaction
Practice Problem: Reaction Order Determination
Integrated Rate Law and Half Life
Integrated Rate Laws (Applying Calculus to get Time Dependence)
• Rate law: Rate = k[A]
• Integrated rate law: ln[A]t = −kt + ln[A]o
• A graph of first order:
– ln[A] versus time results in a straight line
• where slope = −k
• y-intercept = ln[A]o
• Rate constant: k = s–1
D[A]
Dt– = k[A]
Integrated Rate Laws (Applying Calculus to get Time Dependence)
First Order Problem
In acidic aqueous solution, the purple complex ion Co(NH3)5Br2+ undergoes a slow reaction in which the bromide ion is replaced by a water molecule, yielding the pinkish-orange complex ion
Co(NH3)5(H2O)3+:
Co(NH3)5Br2+(aq) + H2O(l) → Co(NH3)5(H2O)3+(aq) + Br−(aq)
Purple Pinkish-orange
The reaction is first order in Co(NH3)5Br2+, the rate constant at 25 °C is 6.3 × 10−6s−1 and the initial concentration of Co(NH3)5Br2+ is 0.100 M.
(a) What is the molarity of Co(NH3)5Br2+ after a reaction time of 10.0 h?
(b) How many hours are required for 75% of the Co(NH3)5Br2+ to react?
Second-Order Reactions
• Rate law: Rate = k[A]2
• Integrated rate law: 1/[A]t = kt + 1/[A]o
• A graph of second order: 1/[A] versus time results in a straight line
• where slope = k
• y-intercept = 1/[A]o
• Rate constant: k = M–1 · s–1
Zero-Order Reactions
• Rate law: Rate = k[A]0 = k
• Integrated rate law: [A]t = −kt + [A]o
• A graph of zero order: [A] versus time results in a straight line
• where slope = −k
• y-intercept = [A]o
• Rate constant: k = M · s–1
Half-Life of Reactions
• NOTE: The half-life, t½, of any reaction is the length of time it takes for the concentration of the reactant to fall to ½ its initial value.
• The half-life of the reaction depends on the order of the reaction.
• First-order half-life – The half-life of a first-order reaction is constant.