Consider the reaction: 2 H 2 O 2 (aq) → 2 H 2 O(l ) + O 2 ( g) The graph shows the concentration of H 2 O 2 as a function of time. Use the graph to calculate each quantity: c. the instantaneous rate of formation of O 2 at 50 s

Welcome back everyone. In this example, we need to estimate the instantaneous rate of formation of oxygen at 70 seconds for the reaction below based on our given graph. So we have two moles of di nitrogen pent oxide which produces four moles of nitrogen dioxide and one mole of oxygen. And according to our graph, we have time given in seconds on the X axis and the concentration of oxygen on our Y axis. And according to the prompt, the instantaneous rate of formation is at 70 seconds. So we wanna go ahead and refer to the following formula where we would find the rate of oxygen being formed, which is going to equal the change in formation of oxygen divided by the change in time that it takes the oxygen to form. And since we're using delta, we would say that we would take the final concentration of oxygen minus the initial concentration of oxygen and then divided by our final time T two minus the initial time being T one. So plugging in what we know for our rate, we would say that our final concentration of oxygen. So because we have to refer to the instantaneous rate of oxygen being at 70 seconds, we're going to look at the time that occurs after 70 which according to our graph is 80 seconds. So we would use 80 seconds as our final time. And that goes in our denominator. This will correspond to the final concentration of oxygen, which we can see is at this point of our Y axis. And as a percentage that's about 0.79% which we will convert to a decimal as 0.79. Now we would subtract from our initial concentration of oxygen which will occur because again, the prompt says the instantaneous rate is going to be for 70 seconds. We want to look at the time before 70 seconds, which on a graph is going to be at 60 seconds here and looking for the concentration of oxygen at 60 seconds, we would see that this corresponds to about point or 65% which we would convert to about 0.65. So we have about 0.65 concentration of oxygen at 60 seconds. So we need to just add that subtraction sign in the denominator and plugging this quo into our calculators. We would get that our rate is going to equal a value of seven times 10 to the negative third power. And recall that our units for concentration is molar and we still have per second in our denominator. And so this will actually complete this example as our final answer for our instantaneous rate of formation of oxygen at 70 seconds. So I hope that everything I explained was clear. If you have any questions, leave them down below and I will see everyone in the next practice video.

Ch.14 - Chemical Kinetics

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Tro 4th Edition

Ch.14 - Chemical Kinetics

Problem 34c

Chapter 14, Problem 34c

Consider the reaction: 2 H₂O₂(aq) → 2 H₂O(l ) + O₂( g) The graph shows the concentration of H₂O₂ as a function of time.
Use the graph to calculate each quantity: c. the instantaneous rate of formation of O₂ at 50 s

Verified step by step guidance

Determine the slope of the tangent line to the curve at 50 seconds on the graph of H_2O_2 concentration versus time.

Use the stoichiometry of the reaction: 2 H_2O_2(aq) → 2 H_2O(l) + O_2(g) to relate the rate of disappearance of H_2O_2 to the rate of formation of O_2.

The rate of formation of O_2 is half the rate of disappearance of H_2O_2, due to the stoichiometric coefficients in the balanced equation.

Calculate the instantaneous rate of formation of O_2 by taking half of the slope determined in the first step.

Express the rate in appropriate units, typically mol/L·s, based on the units used in the graph.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reaction Rate

The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It can be expressed as the change in concentration of a reactant or product over time. Understanding how to calculate reaction rates is essential for analyzing chemical kinetics and determining how quickly a reaction proceeds.

Instantaneous Rate

The instantaneous rate of a reaction is the rate at a specific moment in time, rather than over an interval. It can be determined by taking the slope of the tangent line to the concentration vs. time graph at the desired time point. This concept is crucial for accurately assessing how fast a product is being formed or a reactant is being consumed at any given moment.

Stoichiometry

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction, based on the balanced chemical equation. In the given reaction, the stoichiometric coefficients indicate that for every 2 moles of H2O2 decomposed, 1 mole of O2 is produced. This relationship is vital for converting the rate of formation of one substance into the rate of formation of another.