The Arrhenius Equation and Activation Energy Essay Example

The Arrhenius Equation and Activation Energy Paper In this lab, our task is to determine how different degrees of temperature affect reaction rates.  A Swedish chemist, named Svante Arrhenius discovered the relationship between temperature and reaction rate. In finding this relationship a new equation was formed called the Arrhenius Equation:  Reaction rate constant k = A e -Ea/RT  The factor A represents the frequency of collisions between two molecules in the proper orientation for reactions to occur. The value of A is determined by experiment and will be different for every reaction. The value of the exponential term e -Ea/RT describes the fraction of molecules with the minimum energy required to react, R is the gas constant, 8.314 J/mol-K, T is the temperature in Kelvin and Ea is the activation energy. Activation energy of a reaction is the minimum amount of energy needed to start the reactions. In order to understand and make use of this equation, we must include the Collision Theory. Collision Theory states that in order for a reaction to occur, two molecules must collide in the proper orientation and posses a minimum amount of energy to react. The Arrhenius equation accounts for all of the requirements of Collision Theory.  The Arrhenius equation can be rearranged and combined to determine the activation energy for a reaction based on how the rate constant changes with temperature: In this lab, we will be calculating the rate constants for each of the four temperatures. The four temperatures include: 23, 40, 50, and 60 degrees Celsius. After the rate constant is found for these temperatures, we will use the Arrhenius Equation to solve for Ea and A by an analytical approach. Additionally we will use a graphically approach to solve for these values. The value found for Ea analytically is 9.20 X 104 J/Mol and the value for Ea found graphically is 8.51 X 10 4 J/Mol. We will write a custom essay sample on The Arrhenius Equation and Activation Energy specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on The Arrhenius Equation and Activation Energy specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on The Arrhenius Equation and Activation Energy specifically for you FOR ONLY $16.38 $13.9/page Hire Writer The difference between the two is 6873 J/Mol. The value of 9.20 X 104 J/Mol was found experimentally, while the value of 8.51 X 10 4 J/Mol was found by using experimental data to find the best-fit equation for the line. Because this was a best-fit equation done by a computer working with the experimental data a difference is expected. It should be noted that the difference of the two figures is relatively small. Conclusion: In this lab, we experimentally tested how reaction rates change with varying degrees of temperature. We tested this by measuring out specific volumes of reactants, when the final reactant was placed in the flask we started the stopwatch. We were able to time the reaction visually by the change in color, once the reactant color turned clear the reaction was over and the stopwatch was stopped. We did this four times with the variable being the temperature of the water baths that the flasks were in. The first run was done with no water bath, thus at room temperature of 23à ¯Ã‚ ¿Ã‚ ½C and the other three runs at 40, 50 and 60à ¯Ã‚ ¿Ã‚ ½ C. When we solved for Ea1 the value was 8.94 X102 KJ/Mol this represents the two lowest temperature and the value of Ea2 was 9.45 X 101 KJ/Mol for the two highest temperatures. Our data supports the idea that as temperature increases the rate increased, this was the true for all four runs. As with any experiment there is always a margin of error, in this case we were not working in a closed environment, and the fact that we took the flask out of the water baths before reading the final temperature occur twice which could possible provide an error. Prior to doing this lab, I have been told as well as have read that it is a clear understanding in the scientific world that a change of 10à ¯Ã‚ ¿Ã‚ ½C will double the rate of a reaction. We tested this in this lab, and once again this understanding has been substantiated. This experiment emphasized that the Arrhenius equation is a proving powerful tool for predicting reaction rates over a wide range of temperatures. After a final analysis of our data, I feel confident that our experiment was a success. My understanding of this concept is more firmly in place than prior to this experiment. References: Moore, John W., et al. The Chemical World Concepts and Applications. Orlando: Harcourt Brace Company 1994. Silberberg, Martin S., 2000. Chemistry: The Molecular Nature of Matter and Change. Third Edition. New York: McGraw-Hill Higher, 2000.

White Noise Process Definition

White Noise Process Definition The term white noise in economics is derivative of its meaning in mathematics and in acoustics. To understand the economic significance of white noise, its helpful to look at its mathematical definition first.   White Noise in Mathematics Youve very probably heard white noise, either in a physics lab or, perhaps, at a sound check. Its that constant rushing noise like a waterfall. At times you may imagine youre hearing voices or pitches, but they only last an instant and in reality, you soon realize, the sound never varies.   One math encyclopedia defines white noise as A generalized  stationary stochastic process  Ã‚  with constant  spectral density. At first glance, this seems less helpful than daunting. Breaking it down into its parts, however, can be illuminating.   What is a stationary stochastic process? Stochastic means random, so a stationary stochastic process is a process that is both random and never varying its always random in the same way. A stationary stochastic process with constant spectral density is, to consider an acoustic example, a random conglomeration of pitches every possible pitch, in fact which is always perfectly random, not favoring one pitch or pitch area over another.   In more mathematical terms, we say that the nature of the random distribution of pitches in white noise is that the probability of any one pitch is no greater or less than the probability of another. Thus, we can analyze white noise statistically, but we cant say with any certainty when a given pitch may occur.   White Noise in Economics in the Stock Market White noise in economics means exactly the same thing. White noise is a random collection of variables that are uncorrelated. The presence or absence of any given phenomenon has no causal relationship with any other phenomenon.    The prevalence of white noise in economics is often underestimated by investors, who often ascribe meaning to events that purport to be predictive when in reality they are uncorrelated. A brief perusal of web articles on the direction of the stock market will indicate each writers great confidence in the future direction of the market, beginning with what will happen tomorrow to long-range estimates.   In fact, many statistical studies of the stock markets have concluded that although the direction of the market may not be entirely random, its present and future directions are very weakly correlated, with, according to one famous study by future Nobel Laureate economist Eugene Fama, a correlation of less than 0.05. To use an analogy from acoustics, the distribution may not be white noise exactly, but more like a focused kind of noise called pink noise. In other instances related to market behavior, investors have what is nearly the opposite problem: they want statistically uncorrelated investments to diversify portfolios, but such uncorrelated investments are difficult, perhaps close to impossible to find as world markets become more and more interconnected. Traditionally, brokers recommend ideal portfolio percentages in domestic and foreign stocks, further diversification into stocks in large economies and small economies and different market sectors, but in the late 20th and early 21st centuries, asset classes that were supposed to have highly uncorrelated results have proven to be correlated after all.