Answered: 2. A sample of a substance containing…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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2. A sample of a substance containing only carbon, hydrogen, and oxygen has mass x in grams. It is burned and produces y grams of carbon dioxide and z grams of water. What is the empirical formula of the substance?

Leave your answer as a system of two equations in terms of constants (x, y, z), unknowns (a, b, c), and atomic masses from the periodic table. (no point in giving you numbers for x, y, z or having you do linear algebra – get used to variables!)

Hint: Write the chemical equation giving your carbohydrate subscripts a for C, b for H, and c for O.

Hint: Find the coefficients of this equation in terms of a, b, and c. For now, leave the coefficient of the hydrocarbon 1.

Hint: One equation will have ratios between the carbohydrate and carbon dioxide; the other, ratios between the carbohydrate and water.

Expert Solution

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The equation for the burning of carbohydrate is:

$\begin{array}{rcl} (\frac{x}{12 a + b + 16 c}) C_{a} H_{b} O_{c} + O_{2} & \to & \frac{y}{44} {CO}_{2} + \frac{Z}{18} H_{2} O \\ The stoichiometric coefficients are calculated as per the given masses . \\ Now, consider the burning of a carbohydrate \\ C_{6} H_{12} O_{6} + 6 O_{2} & \to & 6 {CO}_{2} + 6 H_{2} O \\ C_{12} H_{22} O_{11} + 12 O_{2} & \to & 12 {CO}_{2} + 11 H_{2} O \\ The coefficients are in a pattern, always, such that \\ coefficient of {CO}_{2} & = & O_{2} = No . of cabon atoms \\ coefficient of H_{2} O & = & No . of Oxygen atoms in hydrocarbon = \frac{1}{2} no of Hydrogen atoms \\ Hence, \frac{y}{44} & = & a \\ \frac{Z}{18} & = & c = \frac{b}{2} \end{array}$

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