(a) To find the concentration of N2O5 after 5.00 minutes:
We'll use the integrated rate law equation:
1/[N2O5]_t = 1/[N2O5]_0 + kt
Given:
- Initial concentration [N2O5]_0 = 1.58 mol/L
- Rate constant k = 2.8 × 10^-2 s^-1
- Time t = 5.00 minutes = 5.00 × 60 seconds
Plugging in the values:
1/[N2O5]_t = 1/1.58 + (2.8 × 10^-2) × (5.00 × 60)
[N2O5]_t ≈ 1/9.4
[N2O5]_t ≈ 0.106 mol/L
So, the concentration of N2O5 after 5.00 minutes is approximately 0.106 mol/L.
(b) To find the time it takes for 35.0% of N2O5 to decompose:
We'll use the integrated rate law again:
1/[N2O5]_final = 1/[N2O5]_0 + kt_final
Given:
- Final fraction remaining = 0.35
- Initial concentration [N2O5]_0 = 1.58 mol/L
- Rate constant k = 2.8 × 10^-2 s^-1
Plugging in the values:
t_final = 1/(0.35 × (2.8 × 10^-2))
t_final ≈ 1027.67 seconds
So, it will take approximately 1027.67 seconds for 35.0% of the N2O5 to decompose.
