Arc Length and Angle Problem: As a result of the definition of radians, you can calculate the arc length as the product of the angle in radians and the radius of the circle. Figure 3-4g (above) shows arcs of three circles subtended by a central angle of 1.3 radians. The circles have radii of 1, 2, and 3 centimeters. a. How long would the arc of the 1-cm circle be if you measured it with a flexible ruler? b. Find how long the arcs are on the 2-cm circle and on the 3-cm circle using the properties of similar geometrical figures. c. On a circle of radius r meters, how long would an arc be that is subtended by an angle of 1.3 radians? d. How could you find quickly the length a of an arc of a circle of radius r meters that is subtended by a central angle of measure radians? Write a formula for the arc length.
Chapter 15 Part 2: The Steady State Approximation: o Two limiting cases: Low pressure: When [M] is small, k2>k2[M] and rate is 2ndorder High pressure: When [M] is large, k1[M]>k2 and rate is 1 order Intermediates follow pseudo first-order kinetics Effects of temperature on reaction rates: o Many reactions increase rapidly with T Increase T by 10 degrees, rate doubles o Arrhenius equation states that rate constants depend exponentially on temperature. o k=Ae^-Ea/RT o lnk=lnA-Ea/RT o When plotted with y axis lnk and x axis 1/T, the slope is a negative linear one