The rate of the reaction NO2 + CO → NO + CO2 depends only on the concentration of NO2. The following data were collected:

Question

The rate of the reaction NO₂ + CO → NO + CO₂ depends only on the concentration of NO₂. The following data were collected:

Time (s)	[NO2]0 (M)
0	0.500
1.20 x 103	0.444
3.00 x 103	0.381
4.50 x 103	0.340
9.00 x 103	0.250
1.80 x 104	0.174

Calculate the molarity of NO₂ at 21,813 s after the start of the reaction.

Answer 1

Since the rate depends only on [NO₂], this tells us the reaction is FIRST order in NO₂.

The integrated rate equation for a 1st order reaction is [A] = [A]_oe^-kt

The half life for a first order reaction is t_1/2 = ln 2/k = 0.693/k and we can find the half life by looking carefully at the data in the table.

The t_1/2 = 9.00x10³s as can be seen because that's the time it takes for [NO₂] to be halved. It started at 0.5 M and at 9.00x10³ s it is 0.25 M

Now we can use the expression FR = 0.5ⁿ to find how much NO₂ remains at t = 21,813s (2.1813x104s)

FR = fraction remaining

n = number of half lives elapsed = 2.1813x10⁴ s / 9.00x10³s = 2.42 half lives have elapsed

FR = 0.5^2.42

FR = 0.187 this is the fraction that remains

[NO_2] remaining = 0.187 x 0.5 M = 0.0935 M

The longer, more complex way to get this answer is to use the integrated rate equation and solve for [A], but before doing that you would have to first find k and this is done by t1/2 = 0.693/k.