The following data are obtained for the decomposition of N2O5 at a certain temperature:
2N2O5(g)↔4NO2(g) + O2(g)
Time(s) 0 200 400 600 800
N2O5 (atm) 2.10 1.85 1.63 1.43 1.26
Find the rate constant kobs for this first-order decomposition reaction in sec-1
So far I have two equations that I think are needed: ln([At]/[Ao])=-kt and PV=nRT but how to proceed?
I believe you need to plot the data and determine the slope of the straight line. Plot ln A vs time.
But A stands for concentration..how would i obtain it from the data given?
Consider a .0500m solution.HClO2such that36% of the molecules dissociated when dissolved in water. Calculate the vant Hoff factor for this solution is hclo2 is36% associated
To find the rate constant (kobs) for the first-order decomposition reaction, you can use the integrated rate law for a first-order reaction:
ln([N2O5]t/[N2O5]0) = -kt
In this equation, [N2O5]t is the concentration of N2O5 at time t, [N2O5]0 is the initial concentration of N2O5, k is the rate constant, and t is the time.
Looking at the data, you have the concentrations [N2O5]t at different times (0, 200, 400, 600, and 800 seconds), and the initial concentration [N2O5]0.
You can use any pair of data points to find kobs. Let's use the concentrations at time = 200 seconds and time = 400 seconds:
ln([N2O5]200/[N2O5]0) = -kobs * 200
ln([N2O5]400/[N2O5]0) = -kobs * 400
Now, let's plug in the given values for these concentrations:
ln(1.85/2.10) = -kobs * 200
ln(1.63/2.10) = -kobs * 400
Solving these equations will give you the value of kobs. To solve it mathematically, you can follow these steps:
Step 1: Simplify the equations to isolate the kobs term:
ln(1.85/2.10) = -kobs * 200
ln(1.63/2.10) = -kobs * 400
Step 2: Calculate the natural logarithm of the given values:
ln(0.88095238) = -kobs * 200
ln(0.77619048) = -kobs * 400
Step 3: Solve for kobs by rearranging the equations:
kobs = -ln(0.88095238) / 200
kobs = -ln(0.77619048) / 400
Step 4: Evaluate the numerical values of kobs using a calculator:
kobs = 0.004528 sec^-1 (rounded to 3 decimal places)
Therefore, the rate constant kobs for the first-order decomposition reaction is approximately 0.004528 sec^-1.