### Chemical Reactions and Rates: Reaction Rate CalculationsChemical reactions produce one or more **product** substances from one or more **reactant** substances. If *x* molecules of reactant *X* combine with *y* molecules of reactant *Y* to produce *z* molecules of product *Z*, we write the reaction as:\[ xX + yY \rightarrow zZ \]The reaction rate \( r \) is the rate of change of concentration of one of the products over time. For this example, we can express the rate as:\[ r = \frac{1}{z} \frac{dZ}{dt} = - \frac{1}{y} \frac{dY}{dt} = - \frac{1}{x} \frac{dX}{dt} \]### Example CalculationConsider the reaction where nitrogen gas \(\text{N}_2\) and hydrogen gas \(\text{H}_2\) combine to produce ammonia \(\text{NH}_3\) according to:\[ \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \]Find the rates \( r \), \( \frac{dY}{dt} \), and \( \frac{dX}{dt} \) if ammonia is being produced at a rate of 5 moles per liter per hour.**Steps:**1. Write the given rate of production of \( \text{NH}_3 \): \[ \frac{dZ}{dt} = 5 \text{ mol/Lh} \]2. Calculate the reaction rate \( r \): \[ r = \frac{1}{2} \cdot 5 = 2.5 \text{ mol/Lh} \]3. Using \( r \) to find \( \frac{dY}{dt} \): \[ r = \frac{1}{3} \left( -\frac{dY}{dt} \right) \] \[ -\frac{dY}{dt} = 3 \cdot 2.5 = 7.5 \text{ mol/Lh} \]4. Using \( r \) to find \( \frac{dX}{dt} \): \[ -\frac{dX}{dt} = 2

Nitrogen gas N₂ and hydrogen gas H₂ combine to produce ammonia NH3 according to dy dX 1N₂ + 3H2 → 2NH3. Find r, and if ammonia is being produced at a rate of 5 moles dt dt per liter per hour. T = dY dt dX dt mol Lh mol Lh

Nitrogen gas N₂ and hydrogen gas H₂ combine to produce ammonia NH3 according to dy dX 1N₂ + 3H2 → 2NH3. Find r, and if ammonia is being produced at a rate of 5 moles dt dt per liter per hour. T = dY dt dX dt mol Lh mol Lh

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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