Dinitrogen pentoxide (N2O5) decomposes in chloroform as a solvent to yield NO2 and O2. The decomposition is first order with a rate constant at 45 degrees Celsius of 1.0*10^-5 s^-1.Calculate the partial pressure of O2 produced from 1.00 Liter of 0.600 M N2O5 solution at 45 degrees Celsius over a period of 20.0 h if the gas is collected in a 10.0 Liter container (assume that the products do not dissolve in chloroform.
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To calculate the partial pressure of O2 produced over a period of time, we need to use the rate constant and the concentration of N2O5.
Step 1: Calculate the number of moles of N2O5
Given that the volume of the solution is 1.00 L and the concentration is 0.600 M, we can use the formula:
moles of N2O5 = volume × concentration
moles of N2O5 = 1.00 L × 0.600 M
moles of N2O5 = 0.600 moles
Step 2: Calculate the number of moles of O2 produced
The balanced equation for the decomposition of N2O5 states that 1 mole of N2O5 yields 1 mole of O2. Therefore, the number of moles of O2 produced is also 0.600 moles.
Step 3: Calculate the number of moles of O2 in the 10.0 L container after 20.0 hours
We can use the first-order rate equation to calculate the number of moles of O2 produced over time:
Rate = k × [N2O5]
where k is the rate constant and [N2O5] is the concentration of N2O5.
To find the concentration of N2O5 at a specific time, we use the integrated form of the first-order rate equation:
[N2O5] = [N2O5 initial] × e^(-kt)
where [N2O5 initial] is the initial concentration of N2O5, k is the rate constant, and t is the time.
In this case, [N2O5 initial] is 0.600 M, k is 1.0 × 10^-5 s^-1, and t is 20.0 hours (which needs to be converted to seconds: 1 hour = 3600 seconds).
[N2O5] = 0.600 M × e^(-(1.0 × 10^-5 s^-1) × (20.0 hours × 3600 seconds/hour))
Now, we can calculate the number of moles of O2 produced in the 10.0 L container:
moles of O2 = [O2] × volume
moles of O2 = ([N2O5] - 0) × 10.0 L [Assuming no N2O5 dissolves in chloroform]
moles of O2 = ([N2O5 initial] × e^(-(1.0 × 10^-5 s^-1) × (20.0 hours × 3600 seconds/hour))) × 10.0 L
Step 4: Calculate the partial pressure of O2
Finally, we can calculate the partial pressure of O2 using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since we are given the volume (10.0 L) and the temperature (45 degrees Celsius, which needs to be converted to Kelvin: 45 + 273 = 318 K), we can rearrange the equation to solve for P:
P = (nRT) / V
P = (moles of O2 × R × 318 K) / 10.0 L
Substituting the value for R (0.0821 L · atm / (mol · K)) and the moles of O2 calculated in the previous step, we can find the partial pressure of O2.
P = (moles of O2 × 0.0821 L · atm / (mol · K) × 318 K) / 10.0 L