dinitrogen pentoxide n2o5 decomposes by a first-order decomposition in chloroform solvent to yield NO2 and O2. The rate constant at 45°C is 6.2 x 10^-4 mins^-1. Calculate the volume of O2 obtained from the reaction of 1.00 mol N2O5 at 45°C and 770 mmHg after 20.0 hours.
2 N2O5 = 4 NO2 + O2
Or this balanced equation actually N2O5 = 2 NO2 + 1/2 O2
Something interesting
To calculate the volume of O2 obtained from the reaction of 1.00 mol N2O5, we can use the ideal gas law equation: PV = nRT.
First, let's calculate the number of moles of O2 produced from the decomposition of 1.00 mol of N2O5. According to the stoichiometry of the reaction, 2 moles of N2O5 produce 1 mole of O2. Therefore, 1.00 mol of N2O5 will produce 1.00/2 = 0.50 moles of O2.
Next, we need to convert the given time from hours to minutes since the rate constant is given in minutes. There are 60 minutes in an hour, so 20 hours is equal to 20 * 60 = 1200 minutes.
Now we can use the first-order rate equation to calculate the concentration of N2O5 at t = 1200 minutes. The first-order rate equation is given by:
ln[N2O5]t = -kt + ln[N2O5]0
Where [N2O5]t is the concentration of N2O5 at time t, k is the rate constant, and [N2O5]0 is the initial concentration of N2O5.
To find [N2O5]t, we rearrange the equation:
[N2O5]t = e^(-kt + ln[N2O5]0)
Given that the rate constant k is 6.2 x 10^(-4) mins^(-1), the initial concentration [N2O5]0 is 1.00 mol, and t is 1200 minutes, we can substitute these values into the equation.
[N2O5]t = e^(-6.2 x 10^(-4) * 1200 + ln(1.00))
Now, we can substitute this value of [N2O5]t into the stoichiometry equation to calculate the moles of O2 produced:
moles of O2 = [N2O5]t * (1 mole O2 / 2 moles N2O5)
Finally, we can use the ideal gas law equation to calculate the volume of O2 at 45°C and 770 mmHg. The gas constant R is 0.0821 L·atm/(mol·K), and the temperature T is 45°C converted to Kelvin (45 + 273 = 318 K). The pressure P is given as 770 mmHg.
V = (moles of O2 * R * T) / P
By substituting the values into this equation, you can calculate the volume of O2 obtained from the reaction of 1.00 mol N2O5 after 20.0 hours.