The instantaneous rate of reaction is the concentration change over a small time interval
At the point the point t = 40 s the instantaneous rate of reaction (the rate at which the concentration of A is decreasing) is 0.00325 M/s
Reason:
The given points in the plot of the concentration and time are;
[tex]\begin{array}{|c|cc|}Time \ (s)&&Concentration \ (M)\\0&&0.52\\20&&0.43\\40&&0.35\\60&&0.29\\80&&0.24\\100&&0.20\end{array}\right][/tex]
The slope of the curve at a point = The instantaneous rate of reaction
The slope of the curve at a point = The slope of the tangent to the curve at the point
The point at which the (tangent) line touches the curve is (40, 0.35)
The y-intercept of the tangent line is (0, 0.48)
The slope of the equation of the tangent line is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]Slope, \, \mathbf{m} \ of \, the \ tangent \, line =\dfrac{0.35-0.48}{40-0} = -0.00325[/tex]
Equation of the tangent line is y = -0.00325·x + 0.48
Therefore, by transitive property of equality, the rate of the reaction is -0.00325 M/s
The concentration of A in the reaction is decreasing at a rate of 0.00325 M/s at the point the point t = 40 s
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