For the decompostion of gaseous dinitrogen pentaoxide, 2N2O5(g)--->4NO2(g) +O2(g) . The rate constant is k=2.8 x 10^-3 at 60 degrees C. The initial concentration of N2O5 is 2.45 mol/L.
What is (N2o5) after 5.00 min?
What fraction of the N2o5 has decomposed after 5 min?
You omitted the units for the rate constant. It's a first order reaction.
ln(No/N) = kt
No = 2.45 mol
N = ?
k from above
t = 5 min but since k is per second, 5 minutes must be converted to seconds.
To find the concentration of N2O5 after 5.00 minutes, we can use the integrated rate law for a first-order reaction:
ln([N2O5]t/[N2O5]0) = -kt
where [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.
Given:
[N2O5]0 = 2.45 mol/L
k = 2.8 x 10^-3 min^-1 (Note: we need to convert it to min^-1 since the time is given in minutes.)
t = 5.00 min
Substituting the values into the equation, we have:
ln([N2O5]t/2.45) = -(2.8 x 10^-3 min^-1) * (5.00 min)
Now, let's solve for [N2O5]t.
First, rearrange the equation:
[N2O5]t/2.45 = e^(-2.8 x 10^-3 min^-1 * 5.00 min)
[N2O5]t = 2.45 * e^(-2.8 x 10^-3 min^-1 * 5.00 min)
Calculating the right side of the equation:
[N2O5]t = 2.45 * e^(-1 * 2.8 x 10^-3 * 5.00)
[N2O5]t ≈ 2.45 * e^(-1.4 x 10^-2)
[N2O5]t ≈ 2.45 * 0.986
[N2O5]t ≈ 2.41 mol/L
Therefore, the concentration of N2O5 after 5.00 minutes is approximately 2.41 mol/L.
To find the fraction of N2O5 that has decomposed after 5 minutes, we can use the following equation:
Fraction decomposed = (initial concentration - concentration at time t) / initial concentration
Using the given values:
Fraction decomposed = (2.45 - 2.41) / 2.45
Fraction decomposed ≈ 0.016 / 2.45
Fraction decomposed ≈ 0.0065
Therefore, approximately 0.0065 (or 0.65%) of the N2O5 has decomposed after 5 minutes.
To find the concentration of N2O5 after 5.00 min, we can use the integrated rate law for a first-order reaction, which is:
ln[N2O5]t = -kt + ln[N2O5]0
Where [N2O5]t is the concentration of N2O5 at time t, k is the rate constant, [N2O5]0 is the initial concentration of N2O5, and ln is the natural logarithm.
Given that the rate constant (k) is 2.8 x 10^-3 at 60 degrees C, and the initial concentration ([N2O5]0) is 2.45 mol/L, we can substitute these values into the equation:
ln[N2O5]5.00 min = -(2.8 x 10^-3 mol/L min^-1)(5.00 min) + ln(2.45 mol/L)
Calculating this equation will give us the natural logarithm of the concentration of N2O5 after 5.00 min.
To determine the fraction of N2O5 that has decomposed after 5 min, we can use the following equation:
Fraction decomposed = (Initial concentration - Concentration at time t) / Initial concentration
Substituting the known values, we can calculate the fraction decomposed.
Keep in mind that the given rate constant is at 60 degrees C, so if the reaction is not at this temperature, you may need to adjust the rate constant using the Arrhenius equation.