Question

Understanding the high-temperature formation and breakdown of the nitrogen oxides is essential for controlling the pollutants generated by car engines. the second-order reaction for the breakdown of nitric oxide to its elements has rate constants of 0.0796 l/mol-s at 737°c and 0.0815 l/mol-s at 947°c. what is the activation energy of this reaction? give your answer in scientific notation.

Answer 1

To find the activation energy for the breakdown of nitric oxide, we use the Arrhenius equation and the two given rate constants along with their temperatures converted to Kelvin. The formula allows us to calculate the activation energy, which must be presented in scientific notation.

Step-by-step explanation:

To calculate the activation energy of the breakdown of nitric oxide into its elements, we can use the Arrhenius equation:

k = A * e(-Ea/R*T)

where,

k is the rate constantA is the frequency factorEa is the activation energyR is the gas constant (8.314 J/(mol*K))T is the temperature in Kelvin

The temperatures provided need to be converted from Celsius to Kelvin:

• 737°C + 273.15 = 1010.15 K
• 947°C + 273.15 = 1220.15 K

Now, let's apply the two provided rate constants at their respective temperatures into the Arrhenius equation:

ln(k2/k1) = (Ea/R) * (1/T1 - 1/T2)

By plugging in the known values, we get:

ln(0.0815/0.0796) = (Ea/8.314) * (1/1010.15 - 1/1220.15)

The calculation will give us the value of Ea. Keep in mind to use proper units to get the answer in Joules per mole.

By solving this equation, we will obtain the activation energy of the reaction in scientific notation.

Answer 2

Answer is: activation energy of this reaction is 1062 J/mol.
Arrhenius equation: ln(k₁/k₂) = Ea/R (1/T₂ - 1/T₁).
k₁ = 0,0796 l/mol·s.
k₂ = 0,0815 l/mol·s.
1/T₁ = 1/737+273 = 0,00099 1/K.
1/T₂ = 1/947+273 = 0,00081 1/K.
ln(0,0796/0,0815) = Ea/8,3145 J/Kmol · (-0,00018 1/K).
0,023 / 0,00018 = Ea/8,3145 J/Kmol.
Ea = 1062 J/mol.