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The probability that a patient recovers from a | Ch 6 - 6.27

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 6.27 Chapter 6

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 6.27

The probability that a patient recovers from a delicate heart operation is 0.9. Of the next 100 patients having this operation, what is the probability that (a) between 84 and 95 inclusive survive? (b) fewer than 86 survive?

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Common ion effect: the presence of an ion decreases the solubility of a compound containing that ion. Ex. An 0.1 M solution of silver nitrate will dissolve less silver chloride than a solution of pure water. When making the ICE table, be sure to write in the initial concentration of whatever ion is already present in the solution. Other than that, the problem is worked no differently than when you are dissolving a compound in pure water. + An Arrhenius acid produces hydronium ion (H O ) in 3ater. An Arrhenius base produces hydroxide ion (OH ) in water. A Bronsted-Lowry acid is a proton donor. A Bronsted-Lowry base is a proton acceptor. An acid-base conjugate pair differs by one proton, i.e. HF/F , NH /NH . 4 3 2- NOT an acid/base conjugate pair: H SO /S2 . 4hese4two compounds do not differ by one proton. They differ by two protons. The equilibrium constant for the auto-ionization of water is K =10 . whe expression + - is Kw=[H ][OH ], where the concentrations of H and OH are equal. The pH is calculated as –log[H ] and is on a scale from 1 to 14, with 1 being the most acidic (highest concentration of hydrogen) and 14 being the most basic (highest concentration of hydroxide). Pure water has a pH of 7. The pOH is - calculated as –log[OH ]. The pH and pOH sum to 14, so it is easy to convert from one to the other. Strong acids dissociate completely in water and have K=infinity. The six strong acids are:  HCl  HBr  HI  HNO 3  HClO 4  H 2O 4 Strong bases dissociate completely in water and have K=infinity. Almost all bases are strong. Ammonia is a weak base. When given a problem, assume a strong base unless you are told otherwise. Sample problem: You mix 20 mL 0.1 M HCl with 15 mL 0.2 M HClO . What is th4 pH of the resulting solution Since pH only takes into account the hydrogen ion concentration, we will ignore the fact that two different acids are used. We don’t care about chloride and perchlorate ions because they don’t affect the pH. The first step is to calculate the number of moles of hydrogen ion we have. Each acid is a strong acid, so the number of moles of hydrogen will be equal to the number of moles of acid. + 0.1 M HCl * 0.02 L = 0.002 mol HCl = 0.002 mol H + 0.2 M HClO *40.015 L= 0.003 mol HClO = 0.043 mol H 0.002 + 0.003 = 0.005 mol H + The next step is to convert this to molarity. Our total volume of acid is .02 + .015 = . 035 L. .005mol/.035L = .357 M pH=-log[.357]=.845 Is our answer reasonable We are mixing two strong acids, so our pH value should indicate an acidic solution. A pH value of .845 is very acidic. The pH of a weak acid is calculated using the same method used to determine the + concentration of sparingly soluble salts. The concentration of H is determined, and then the pH is determined by taking the negative log of this value. In using the above method, it is often useful to neglect x to save having to use the quadratic equation. X can be neglected when concentration/K > 100.

Step 2 of 3

Chapter 6, Problem 6.27 is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

This full solution covers the following key subjects: . This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. Since the solution to 6.27 from 6 chapter was answered, more than 439 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. The answer to “The probability that a patient recovers from a delicate heart operation is 0.9. Of the next 100 patients having this operation, what is the probability that (a) between 84 and 95 inclusive survive? (b) fewer than 86 survive?” is broken down into a number of easy to follow steps, and 38 words. The full step-by-step solution to problem: 6.27 from chapter: 6 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM.

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The probability that a patient recovers from a | Ch 6 - 6.27