Concentration Graphs: Instantaneous time

[SS2006]

im having troubles with this
the teacher wants us to find hte instantaneous rate of reaction at time 60 seconds , so i trace 60 s to the graph and make a point where it meets. Now i draw a tangent to this point. This is what gets me, how long should this tangent me, because i kow i have to get the slope of this tangent (that will be my asnwer right) so if i don't nkow how long the tangent should be ill get different rise/run results.
i just want quick instructions
thanks!

 

[mrjeffy321]

Ideally, you would want to take the derivative of the equation describing the rate of reaction, but more likely than not, you don’t have that (and/or you don’t know how).
The next best thing would be to draw a tangent line on the point you’re analyzing.
If the tangent line is drawn properly, it shouldn’t matter how long it is drawn because it should have a constant slope, which should be equal to the instantaneous slope of the reaction rate curve.
Draw the line a convenient length for you to make the math easier, and then find the slope.
Slope = Change in Y / change in X
And by change in, I mean, the ending point - the starting point of the X or Y component of the line.

 

[SS2006]

thank you, sir :)

 

[ShawnD]

If you suck at drawing lines, you can make a graph in Excel of the concentration vs time, then have it spit out a trend line. Take the derivative of that equation to get the equation for the reaction rate.
The advantage of doing this is that you get a much more precise value that is based entirely on math instead of being based on the steadiness of your hand, the phase of the moon, how you think the tangent should look, etc. This also takes less time if you planned to make the graph in Excel anyway, which you probably should.

In case you don't know; the derivative (for simple formulae) is made by multiplying the constant of a variable by the variable's exponent, then lowering the exponent by 1. Example: y = x^2 + 5x + 3 has a derivative of y = 2x + 5. Another example: y = 4x^3 + 10 has a derivative of y = 12x^2.