CHAPTER Mathematical preliminaries and Error analysis Introduction In beginning chemistry courses, we see the ideal gas law, PV= NRT which relates the pressure P, volume V, temperature T, and number of moles N of an "ideal"gas. In this equation, R is a constant that depends on the measurement system. Suppose two experiments are conducted to test this law, using the same gas in each case. In the first experiment, P=1.00atm, V=0.100m N=0.00420mol,R=0.08206 The ideal gas law predicts the temperature of the gas to be PV(1.00)(0.100) NR(0.00420)(0.08206) =290.15K=17°C When we measure the temperature of the gas however, we find that the true temperature is 15°C. We then repeat the experiment using the same values of R and N, but increase the pressure by a factor of two and reduce the volume by the same factor. The product PV remains the same, so the predicted temperature is still 17C. But now we find that the actual temperature of the gas is 19C t materially affect the overal leaming eperience. Cengage Learning reserves the right b remove arty oomen may be suppressed from the eBook andor eChapterts). Copynight 2010 Cengage Learning. All Rights Reserved, May no be copied, scanned,CHAPTER 1 Mathematical Preliminaries and Error Analysis Introduction In beginning chemistry courses, we see the ideal gas law, PV = NRT, which relates the pressure P, volume V, temperature T, and number of moles N of an “ideal” gas. In this equation, R is a constant that depends on the measurement system. Suppose two experiments are conducted to test this law, using the same gas in each case. In the first experiment, P = 1.00 atm, V = 0.100 m3 , N = 0.00420 mol, R = 0.08206. The ideal gas law predicts the temperature of the gas to be T = PV NR = (1.00)(0.100) (0.00420)(0.08206) = 290.15 K = 17◦ C. When we measure the temperature of the gas however, we find that the true temperature is 15◦C. V1 V2 We then repeat the experiment using the same values of R and N, but increase the pressure by a factor of two and reduce the volume by the same factor. The product PV remains the same, so the predicted temperature is still 17◦C. But now we find that the actual temperature of the gas is 19◦C. 1 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it