Calculate the pressure

Question

The rate constant for the low pressure decomposition of N₂O₄(g) is 3.60 × 10⁴ L･mol⁻¹･s⁻¹ at 250 K. If the initial pressure of N₂O₄(g) is 35.0 torr at 250 K, calculate the pressure of N₂O₄(g) remaining after 15.0 milliseconds. Assume any reverse reactions are insignificant under these conditions. Note: 760 torr/1 atm.

Answer 1

Given a 2nd order rate constant (r = kC² from the units) the integrated rate law is 1/C₀-1/C = kt

From the IGL we know that C = n/V = P/RT, so (for const T)

C = 1/(1/C₀ - kt) and P/RT = 1/(RT/P₀ -kt) and P = 1/(1/P₀ - kt/(RT))

Use 35/760 atm for P₀, .082 for R and .015 s for t

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