What is the initial rate of th

reaction depicted by this graph? The answer is .02 but i dont know

how to get that answer.Someone explain please!

## Answer

The tangent line should look like a straight line that touches

the curve at only 1 point.

The tangent line to a curve is defined as a line representing the

slope of the curve at the point to which it is the tangent; ie, if

you draw a tangent to the curve at t = 0, the tangent gives you the

slope of the curve at that point.

In concentration/time graphs, the slope of the tangent is equal to

the rate of reaction, and the point where the curve hits the y-axis

is equal to the initial concentration of your reagent.

To explain:

Think about the units on your axes; the y-axis has the units “cm^3

of O2”, and the x-axis has the units “s”.

Now think about the units for a rate of reaction. Well, what are

you looking at when looking at the rate? It’s the rate at which

your reactant is being used over time, so in theory it should be

“some measurement of quantity of reactant / time”.

In this case, you’ll be looking at the rate at which the volume of

oxygen gas is changing over time, or “cm^3/s”. Now, looking back at

your axes units, that would be “y-axis units/x-axis units”.

Now consider that a rate measures the CHANGE in concentration over

the CHANGE in time. That means you’re going to have to have the

change in your concentration divided by the change in time, or “(y2

– y1)/(x2 – x1)”, which is the equation for the slope of a

line.

So, now that you have your line, pick 2 points on that line, and

find the x- and y-coordinates of those points. Then, plug them into

your equation for slope to find the slope of the line, and that’s

your rate.

As we need to find initial rate of reaction, we consider very

small change in time from t=0 to t=5s as this is the smallest time

interval we can get from the graph.

So the corresponding change in the concentration = 0.4 – 0.3 =

0.1 M

Hence the initial rate of the reaction can be given as R = 0.1/5

=0.02 mol L^{-1}s^{-1}

Also we see from the graph that the rate decreases as the time

progresses. Other options are smaller than 0.02 thus making 0.02

the most appropriate answer