AP Chemistry Chemical Kinetics Problem

[Hikari]

Homework Statement

The rate of the reaction was studied at a certain temperature.
O(g) + NO2(g) --> NO(g) + O2(g)
In the first set of experiments, NO2 was in large excess, at a concentration of 1.0 * 10^ 13 molecules/cm3 with the following data collected.
time (s) [O] (atoms/cm3)
0 ......2400
0.01.....1200
0.02.....600
0.03......0

Part (a). Find the reaction order with respect to O. (Explain with graphs)

Part (b) Find the rate constant with respect to O.

Homework Equations

Rate = K[A]
First Order Reaction Integrated Rate Law: ln[A] = -kt + ln[A]0

The Attempt at a Solution

I want to know how to transform the graph/data set into a linear line to find the reaction order (I think it is first order). I think I ln[O] and plot it against time (s) to achieve a linear graph for a first order graph. How do I do that? Do I need to convert atoms/cm3 to mol/L? I tried doing that and it is not looking right. Help would be appreciated!

 

[Chestermiller]

Homework Statement

The rate of the reaction was studied at a certain temperature.
O(g) + NO2(g) --> NO(g) + O2(g)
In the first set of experiments, NO2 was in large excess, at a concentration of 1.0 * 10^ 13 molecules/cm3 with the following data collected.
time (s) [O] (atoms/cm3)
0 ......2400
0.01.....1200
0.02.....600
0.03......0

Part (a). Find the reaction order with respect to O. (Explain with graphs)

Part (b) Find the rate constant with respect to O.

Homework Equations

Rate = K[A]
First Order Reaction Integrated Rate Law: ln[A] = -kt + ln[A]0

The Attempt at a Solution

I want to know how to transform the graph/data set into a linear line to find the reaction order (I think it is first order). I think I ln[O] and plot it against time (s) to achieve a linear graph for a first order graph. How do I do that? Do I need to convert atoms/cm3 to mol/L? I tried doing that and it is not looking right. Help would be appreciated!

You don't have to convert to mol/L. The first three data points are OK, but the 4th data point should be 300 atoms/cc (there must be a typo, or maybe you're supposed to think that the measurement is in the noise at 300 atoms/cc). You can plot the first three points, and leave out the 4th, or you can plot all four, with 300 as the last point. If you plot the first 3 points, they will lie on a straight line on a semi-log plot. If you have Excel, just change the vertical scale to a log scale (which Excel will automatically do for you). You can get the first order rate constant from the slope. Excel will even do a curve fit for you, and provide you with the slope, so that you can know the rate constant immediately.

Chet

 

[Hikari]

Thanks you! I got the equation to be y = -69.315x + 7.7832 without plotting the last point. This means the rate constant is -69.3 respect to [O]. It is negative because the concentration is going down as time increases. Is that correct?

 

[Chestermiller]

Thanks you! I got the equation to be y = -69.315x + 7.7832 without plotting the last point. This means the rate constant is -69.3 respect to [O]. It is negative because the concentration is going down as time increases. Is that correct?

In your equation, there is a negative sign in front of k. So the rate constant should be +69.3/sec.

Chet

 

[DeeNos]

To transform the data into a linear line, you can plot ln[O] (y-axis) against time (x-axis). This will give you a straight line if the reaction is first order with respect to O. If the reaction is second order, the graph will be a curved line.

To convert atoms/cm3 to mol/L, you can use the ideal gas law: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant (0.0821 L*atm/mol*K), and T is the temperature in Kelvin. Rearranging this equation to solve for n, you get n = (PV)/(RT). Since the volume is not given in the problem, you can assume it is constant and cancel it out. Then, n = (P)/(RT). To convert from atoms/cm3 to mol/L, you need to multiply by Avogadro's number (6.022*10^23 atoms/mol). So, the equation becomes n = (P)/(RT) * (6.022*10^23 atoms/mol). This will give you the concentration in mol/L.

For part (a), you can use the integrated rate law for a first order reaction: ln[A] = -kt + ln[A]0. In this case, [A] represents the concentration of O, k is the rate constant, t is time, and [A]0 is the initial concentration of O. You can plug in the values from the data set to solve for k. The slope of the line is -k, so the reaction order with respect to O is 1.

For part (b), once you have solved for k, you can use the rate equation: Rate = k[A]. Again, [A] represents the concentration of O. You can plug in the values from the data set to solve for the rate constant k.