First order, would be natural log of concentration A versus time. If you get a straight line with a negative slope, then that would be first order. For second order, if you graph the inverse of the concentration A versus time, you get a positive straight line with a positive slope, then you know it's second order.
When the lnk (rate constant) is plotted versus the inverse of the temperature (kelvin), the slope is a straight line. The value of the slope (m) is equal to -Ea/R where R is a constant equal to 8.314 J/mol-K.
| T (K) | k (s-1) |
|---|
| 328 | 7.59 x 10-4 |
| 338 | 2.40 x 10-3 |
Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
A rate law shows how the rate of a chemical reaction depends on reactant concentration. For a reaction such as aA → products, the rate law generally has the form rate = k[A]â¿, where k is a proportionality constant called the rate constant and n is the order of the reaction with respect to A.
The rate constant is the reaction rate divided by the concentration terms. What is k in the rate law equation? A rate constant.
The order of the reaction is second, and the value of k is 0.0269 M-2s-1. Since the reaction order is second, the formula for t1/2 = k-1[A]o-1. This means that the half life of the reaction is 0.0259 seconds.
| 1/Concentration(M-1) | Time (s) |
|---|
| 3 | 30 |
Rate laws or rate equations are mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In general, a rate law (or differential rate law, as it is sometimes called) takes this form: rate=k[A]m[B]n[C]p…
Rate constant 'k' of a reaction is defined as the rate of reaction when the concentration of the reactant(s) is unity. / or Rate constant is the proportionality factor in the rate law.
To find the units of a rate constant for a particular rate law, simply divide the units of rate by the units of molarity in the concentration term of the rate law.
A first-order reaction depends on the concentration of one reactant, and the rate law is: r=−dAdt=k[A] r = − dA dt = k [ A ] .
The equation of line k is y=mx+b, where m and b are constants.
In the xy-plane, line k is a line that does not pass through the origin.
What is the slope of line k? To find the slope of a line perpendicular to a given line, we must take the negative reciprocal of the slope of the given line. Thus the slope of line k is the negative reciprocal of 2/5 (slope of line m), which is -5/2.
Equations in point-slope form look like this: y - k = m(x - h) where m is the slope of the line and (h, k) is a point on the line (any point works). To write an equation in point-slope form, given a graph of that equation, first determine the slope by picking two points.
