The reaction NO2(g) + NO2(g) → N2O4(g) is second order with a rate constant of 0.044 /M·s at a particular temperature and pressure. If the initial concentration of NO2(g) is 0.100 M, what is the concentration of NO2 after 20 minutes?
1/A - 1/Ao = akt
To find the concentration of NO2 after 20 minutes, we can use the second-order rate equation, which is given by:
1 / [NO2] - 1 / [NO2]0 = kt
Where [NO2] is the concentration of NO2 at a specific time, [NO2]0 is the initial concentration of NO2, k is the rate constant, and t is the time.
Rearranging the equation, we have:
1 / [NO2] = kt + 1 / [NO2]0
We can substitute the given values into the equation:
k = 0.044 /M·s
[NO2]0 = 0.100 M
t = 20 minutes = 20 * 60 seconds = 1200 seconds
Plugging these values into the equation:
1 / [NO2] = (0.044 /M·s) * (1200 s) + 1 / 0.100 M
Simplifying the equation:
1 / [NO2] = 52.8 + 10
1 / [NO2] = 62.8
Taking the reciprocal of both sides:
[NO2] = 1 / 62.8
[NO2] = 0.0159 M
Therefore, the concentration of NO2 after 20 minutes is approximately 0.0159 M.