# The blue curve is the plot of the data. the orange line is tangent to the blue curve at t = 40 s.

The blue curve is the plot of the data. The orange line is tangent
to the blue curve at t = 40 s.
The blue curve is the plot of the data. The orange line is tangent
to the blue curve at t = 40 s. The blue curve is the plot of the data. The orange line is tangent to the blue curve at t = 40 s.

General guidance

Concepts and reason
This problem is based on the concept of chemical kinetics.
Kinetics tells us that how fast or slow does a chemical reaction take place.
Instantaneous rate of reaction is calculated by the graph between reactant/product concentration and time.

Fundamentals

The rate of a reaction is the rate of change of concentration of reactants or products with respect to time.
For a reaction as follows:

Here, A and B are reactant and product respectively.
The rate of a reaction is mathematically expressed as follow:

Here, r is the rate of reaction, is the rate of change of concentration of reactants and dt is the change of time.
The slope of a line is as follows:

Here, m is the slope of the line, and are two y coordinates, and are two x coordinates on the line.

Step-by-step

Step 1 of 2

To determine instantaneous rate of reaction at time equal to 40 seconds, a tangent is drawn at this point. The orange line shown below is the required tangent at .

Here the slope of the tangent at gives out the instantaneous rate of reaction at this point.

Calculate the instantaneous rate of reaction at

Step 2 of 2

Instantaneous Rate is equal to the slope of the tangent line at

Substitute 0.48 M for, 0.16 M for, 0 s for and 92 s for in above equation as follows:

The approximate instantaneous rate of reaction at is .

The instantaneous rate is the rate at a point in the plot at a particular time. Instantaneous rate of reaction is calculated by the graph between reactant/product concentration and time.

The formula for slope can be wrongly taken as follows:

But the correct formula is as follows:

The approximate instantaneous rate of reaction at is .

The approximate instantaneous rate of reaction at is .

A →B
d r=- dt
xx – –
t = 40 s
[A] (M) 0.52 0.48 0.44 0.40 0.36 0.32 0.28 0 24 0.20 0.164 0 10 20 30 40 50 60 70 80 90 100 t(s)
t = 40 s
t = 40 s.
t = 40 s.
xx – –
) (0.48 M -0.16 M Os-92 s = 3.478×10- M/s
=%+} +
xx – –
t=40s
3.478×10- M/s
t=40s
3.478×10- M/s
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