The breakdown of p-nitrophenylphosphate at pH 2.6 is a first order hydrolysis process..
a) 12.5mmol of NPP were dissolved in 200mL of water at 77degrees celcius after 50mins the amount of NPP dropped to 10mmol. Calculate the average rate of this reaction and the rate constant for this process.
B) using the arrhenius equation (given A=6 10^11 s^-1) compute the activation energy of this reaction.
avg rate = (12.5-10)/50 min = ? mM/min.
rate = k(NPP). You know NPP initially and the rate, solve for k.
Plug all of this into the Arrhenius equation an solve for activation energy.
for the part rate= k(NPP) what are the units of measurements at the end ?
To calculate the average rate of the reaction and the rate constant, we can use the formula for a first-order reaction:
Rate = k[NPP]
Where:
- Rate is the rate of the reaction (in mol/L*s),
- k is the rate constant (in s^-1),
- [NPP] is the concentration of NPP (in mol/L).
a) To calculate the average rate of the reaction, we use the formula:
Average Rate = (Change in concentration of NPP) / (Change in time)
Given:
Initial concentration of NPP, [NPP]₀ = 12.5 mmol / 0.200 L = 62.5 mmol/L
Final concentration of NPP, [NPP]ₜ = 10 mmol / 0.200 L = 50 mmol/L
Time, t = 50 mins = 50 min * (1 hour / 60 min) = 0.8333 hours
Change in concentration of NPP = [NPP]ₜ - [NPP]₀ = 50 mmol/L - 62.5 mmol/L = -12.5 mmol/L
Average Rate = (-12.5 mmol/L) / (0.8333 hours) = -15 mmol/(L*h)
Note: The negative sign represents the decrease in concentration.
b) To calculate the rate constant (k), we can use the rearranged formula for a first-order reaction:
k = (ln([NPP]₀) - ln([NPP]ₜ)) / t
Given:
[NPP]₀ = 62.5 mmol/L
[NPP]ₜ = 50 mmol/L
t = 0.8333 hours
k = (ln(62.5 mmol/L) - ln(50 mmol/L)) / 0.8333 hours
Now, we'll use the Arrhenius equation to calculate the activation energy of the reaction:
k = A * e^(-Ea/RT)
Given:
A = 6 × 10^11 s^-1 (rate constant pre-exponential factor)
R = 8.314 J/(mol*K) (ideal gas constant)
T = 77 + 273 = 350 K (temperature in Kelvin)
We can rearrange the equation to solve for the activation energy (Ea):
ln(k/A) = -Ea/RT
Now, we can substitute the values into the equation and solve for Ea.