The Following Table Shows the Concentration (In Mol/L) of a Certain

question 58

Essay

The following table shows the concentration (in mol/L) of a certain chemical in terms of reaction time (in hours) during a decomposition reaction. $$\begin{array} { | l | c | c | c | c | c | c | } \hline \text { Time (hours) } & 0 & 5 & 10 & 20 & 30 & 50 \\\hline \text { Concentration (mol/L) } & 2.32 & 1.86 & 1.49 & 0.98 & 0.62 & 0.25 \\\hline\end{array}$$ (a) Find the average rate of change of concentration with respect to time for the following time intervals:
(i) [0, 5]
(ii) [10, 20]
(iii) [30, 50]
(b) Plot the points from the table and fit an appropriate exponential model to the data.(c) From your model in part (b), determine the instantaneous rate of change of concentration with respect to time.(d) Is the rate of change of concentration increasing or decreasing with respect to time? Justify your answer.

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Definitions:

Normal Profit

Normal profit occurs when a firm's total revenue is equal to its total costs, including the opportunity costs of capital, providing no incentive for entry or exit in the industry.

Yearly Licensing Fee

An annual charge paid to obtain the rights to use a particular piece of intellectual property, software, or other specific products/services.

Market Price

The ongoing rate at which an asset or service is offered for buying or selling in a certain market.

Short Run

A period in economics during which at least one input or resource is fixed, limiting immediate capacity adjustments.