The blue curve is the plot of the data. The straight orange line is tangent to the blue curve at t = 40 s. A plot has the concentration of A in molar on the y axis and time in seconds on the x axis. A curve contains the points (0, 0.52), (20, 0.43), (40, 0.35), (60, 0.29), (80, 0.24), and (100, 0.20). A line touches the curve at (40, 0.35) and has a y intercept of (0, 0.48). Approximate the instantaneous rate of this reaction at time t = 40 s.

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;

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;

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

Learn more about the instantaneous rate of reaction here:

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  0.00325 moles/liter/second

Explanation:

The tangent line has a slope of (y2 -y1)/(x2 -x1) = (0.35-0.48)/(40-0) = -0.00325.

The rate of the reaction is about 0.00325 moles/liter/second.

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This is the rate of decrease of the concentration of A.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west