Using the following data, determine the initial rate by calculating the slope of the tangent line at time zero.
Time (s). [I2] (mM)
0. 0
20. 0.009
40. 0.017
60. 0.023
80. 0.029
100. 0.034
120. 0.039
140. 0.043
160. 0.046
180. 0.049
I can't figure out how to make a tangent line at time zero. Rate of the reaction = 8.59 x10^-7 M/s.
Is it just finding the slope? I made a chart in excel, it gave the y=mx+b: y = 0.0003x + 0.0048, R^2 = 0.9719.
Is that the slope ( y = 0.0003x + 0.0048)?
Please any help would be greatly appreciated.
Is calculating the sloope of the tangent line the same as calculating the slope? (y2-y1) / (x2/x1)
for instance if i took the points 60, 0.023 for X1Y1 and points 100, 0.034 for X2Y2, the slope of the line would be :
(0.034-0.023) / (100-60) = 0.011/40 = 0.000275 (the slope) - m
y = 0.000275x + b?
Nope, it is not linear, it is a curve whose slope decreases.
AT zero, that means the initial slope.
your first slope is .009/20=.00045mmoles/s
or 4.5E-7moles/sec.
At the end, between 160-180 sec
rate=.003/20=.00015E-3=1.5E-7Mol/sec
The other way, to get initial slope, is to plot this on a graph, then connect the points (with a french curve, then draw a tangent line at t=0, you should get about what I calculated above.
To determine the initial rate by calculating the slope of the tangent line at time zero, follow these steps:
1. Plot the data points on a coordinate grid with the Time (s) values on the x-axis and [I2] (mM) values on the y-axis.
2. Connect the data points with a smooth curve that best fits the trend of the data. This will give you a graph of the concentration of iodine ([I2]) as a function of time.
3. Identify the point where the curve intersects with the y-axis (Time = 0 s). In this case, the initial concentration of iodine, [I2]₀, is 0 mM.
4. Plot a tangent line that touches the curve at the point where Time = 0 s. The tangent line should only touch the curve at that specific point and not intersect or cross it.
5. Calculate the slope of the tangent line to find the initial rate of the reaction.
Now, looking at the given data, you mentioned that the rate of the reaction is 8.59 x 10^-7 M/s. This value represents the initial rate.
From the equation you provided (y = 0.0003x + 0.0048), it seems like you have performed a linear regression analysis on the data points. However, determining the slope by this method might not accurately represent the initial rate at Time = 0 s.
To find the initial rate using the tangent line approach, it is necessary to consider the specific concentration values of [I2] at Time = 0 s. In this case, the initial concentration of iodine, [I2]₀, is 0 mM.
Therefore, the initial rate of the reaction would be 0 M/s, as there is no change in concentration (initial concentration is zero).
Note: If there is an error in the given data or additional information that wasn't provided, it may affect the accuracy of the calculations.