Question

The following table gives weight gain–time

data for the oxidation of some metal at an elevated temperature.
W (mg/cm2) Time (min)
6.16 100
8.59 250
12.72 1000
(a) Determine whether the oxidation kinetics obey
a linear, parabolic, or logarithmic rate expression.
(b) Now compute W after a time of 5000 min.

Answer 1

Step-by-step explanation:

(a) To determine whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression, we need to plot the weight gain (W) against the square root of time (t), as shown below:

|W (mg/cm2)|Time (min)|Square root of time (sqrt(t))|

|---|---|---|

|6.16|100|10|

|8.59|250|15.81|

|12.72|1000|31.62|

Plotting W against sqrt(t) gives us a straight line, which indicates that the oxidation kinetics obey a linear rate expression.

(b) To compute W after a time of 5000 min, we can use the equation of the line we obtained in part (a):

W = mt + bwhere m is the slope of the line, b is the y-intercept, and t is the time in minutes.

From the plot, we can see that the slope of the line is:

m = (12.72 - 6.16) / (1000 - 100) = 0.00856And the y-intercept is:

b = 6.16 - 0.00856 x 100 = 5.28Therefore, for a time of 5000 min:

W = 0.00856 x 5000 + 5.28 = 49.88 mg/cm2So the weight gain after 5000 min is approximately 49.88 mg/cm2.