** Instantaneous Rate** is the rate a reaction at any particular point in time.

Instantaneous Rate

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concept

## Instantaneous Rate Concept 1

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instantaneous rate is the rate of a reaction at any particular point in time. And we're going to say here that calculated using the slope of the tangent line to the curb of that point is the way we obtain our instantaneous rate. So if we're given basically a plot of Y and X coordinates, we can use that to figure out the slope which will be equal to our instantaneous rate. Now we're going to say while the rate of reaction decreases with time because the amount of reactant is decreasing in time are instantaneous rate though remains constant here, if we take a look, we say that if we're given uh points Y and X, we can figure out the slope. Remember that slope is equal to change in y over change in X rise over run this really means Y two minus Y one divided by X two minus x one. Here, we would change, we would keep the change and why as changes in our concentration and our changes in X as changes in time. Now. Here we have the graphical representation of a curve and again, we've used two points in terms of this which would relate to our tangent line. We'd utilize this formula for slope and use that to figure out our instantaneous rate. So just keep this in mind as we start investigating more and more questions dealing with calculating the instantaneous rate of an overall reaction or at any particular point

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example

## Instantaneous Rate Example 1

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determine the instantaneous rate for the fall of reaction. Here we have methanol reacting with hydrochloric acid to produce coral, methane plus water as a liquid. We're given the times for the reaction at different points and from this were also given the change in concentration of hydrochloric acid. Now, since we're given all these times and all these concentrations, remember our times will represent X. And our concentrations will represent Y. From this information, we can figure out our instantaneous rate by determining the slope. So here would be Y two minus Y one over X two minus X one. We're going to say that this is our first time given to us which is zero. So we'll say that this is X- one. And if this is X one then this has to be Y one now X two, we can make the last time taken, which would be 2 47. And if this is X two, then this would be Y two. Now we would take those and plug them in. So we have 1.01 -1.90. And these are in concentration similarity Divided by 2:47.0 0 in seconds. When we plug this in, we get negative 3.60 times 10 to the - polarities per minute. So this will represent our instantaneous rate for the reaction. Notice here that the sign is negative because we can see that the concentration of our reaction over time is indeed decreasing as we expect it to be. So this is the approach we take when they're giving us a list of points for X and Y, we determine what the slope is from these coordinates, and with that we can relate it to our instantaneous rate.

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Problem

Consider the decomposition of dinitrogen pentoxide:2 N_{2}O_{5} (g) → 4 NO_{2} (g) + O_{2} (g)

What is the instantaneous rate of this reaction at 20 seconds?

A

0.0325 M/s

B

0.0270 M/s

C

0.0380 M/s

D

0.015 M/s

Additional resources for Instantaneous Rate

PRACTICE PROBLEMS AND ACTIVITIES (11)

- (c) As a reaction proceeds, does the instantaneous reaction rate increase or decrease?
- The isomerization of methyl isonitrile 1CH3NC2 to acetonitrile 1CH3CN2 was studied in the gas phase at 215 C, ...
- The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2¡CH3Cl1aq2 + H2O1...
- Consider the reaction: H2( g) + Br2( g) ¡ 2 HBr( g) The graph shows the concentration of Br2 as a function o...
- Consider the reaction: H2( g) + Br2( g) ¡ 2 HBr( g) The graph shows the concentration of Br2 as a function of ...
- Consider the reaction: 2 H2O2(aq) ¡ 2 H2O(l ) + O2( g) The graph shows the concentration of H2O2 as a function...
- Use the information in Table 14.1 and Figure 14.1 to estimate the instantaneous rate of appearance of NO2 at ...
- From the plot of concentration–time data in Figure 14.1, estimate: (b) the initial rate of decomposition of ...
- From the plot of concentration–time data in Figure 14.1, estimate: (a) the instantaneous rate of decomposition...
- From a plot of the concentration–time data in Worked Example 14.9, estimate: (b) the initial rate of decompo...
- From a plot of the concentration–time data in Worked Example 14.9, estimate: (a) the instantaneous rate of d...