For the gas phase reaction 2NO2 + F2 �¨ 2NO2F, the rate constant is k= 38 dm3/mol-s at 27 oC. The reaction is first-order in NO2 and first-order in F2. A) Calculate the number of moles of NO2, F2, and NO2F after 10.0 s if 2.00 mol of NO2 is mixed with 3.00 mol of F2 in a 400 dm3 vessel at 27 oC. B) For the system in A, calculate the initial reaction rate and the rate after 10.0 s.
I am stuck on this one, please help.
To solve this problem, we need to use the given rate constant and reactant concentrations to calculate the number of moles of each species after a given time.
Before we start, let's identify the given information:
- Reaction: 2NO2 + F2 → 2NO2F
- Rate constant (k): 38 dm3/mol-s
- Temperature (T): 27 oC
- Initial concentrations: [NO2] = 2.00 mol and [F2] = 3.00 mol
- Volume of the vessel (V): 400 dm3
- Time (t): 10.0 s
A) Calculate the number of moles of NO2, F2, and NO2F after 10.0 s:
1. Convert the temperature to Kelvin:
T (K) = 27 + 273 = 300 K
2. Use the rate constant to calculate the reaction rate:
The rate of the reaction is given by the rate law equation:
rate = k[NO2]^1[F2]^1
Since the reaction is first-order in both NO2 and F2, their exponents are 1.
3. Calculate the reaction rate:
Plugging in the values:
rate = k * [NO2] * [F2]
rate = 38 * 2.00 * 3.00 = 228 mol/dm3-s (mol/dm^3·s)
4. Use the reaction rate and the given time to calculate the moles of each species:
moles NO2 after 10.0 s = [NO2]0 - (rate * t)
= 2.00 - (228 * 10.0)
= 2.00 - 2280
= -2278 mol
moles F2 after 10.0 s = [F2]0 - (rate * t)
= 3.00 - (228 * 10.0)
= 3.00 - 2280
= -2277 mol
moles NO2F after 10.0 s = 2 * (rate * t)
= 2 * (228 * 10.0)
= 2 * 2280
= 4560 mol
Therefore, after 10.0 s, there are approximately -2278 mol of NO2, -2277 mol of F2, and 4560 mol of NO2F in the vessel. Note that negative values indicate a complete consumption of the reactants.
B) Calculate the initial reaction rate and the rate after 10.0 s:
- Initial reaction rate:
The initial reaction rate can be obtained by substituting the initial concentrations into the rate law equation:
rate = k * [NO2] * [F2]
rate = 38 * 2.00 * 3.00
rate = 228 mol/dm3-s (mol/dm^3·s)
- Rate after 10.0 s:
We have already calculated the reaction rate after 10.0 s, which is 228 mol/dm^3·s.
Therefore, the initial reaction rate is 228 mol/dm^3·s, and the rate after 10.0 s is also 228 mol/dm^3·s.