Dinitrogen pentoxide, N2O5, decomposes by a first-order reaction. What is the initial rate of decomposition of N2O5 when 3.6 g of N2O5 is confined in a 0.77 L container and heated to 65°C?
For this reaction, k = 5.2 x 10^-3 s-1 in the rate law (for the rate of decomposition of N2O5).
To determine the initial rate of decomposition of N2O5, we need to use the first-order rate law equation:
Rate = k * [N2O5]
Where:
- Rate is the rate of decomposition
- k is the rate constant
- [N2O5] is the concentration of N2O5
To find the concentration of N2O5, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant
- T is the temperature
First, we need to find the number of moles (n) of N2O5 present in the container.
Step 1: Convert the given mass of N2O5 to moles.
First, we need to determine the molar mass of N2O5.
Nitrogen (N) has a molar mass of 14.01 g/mol.
Oxygen (O) has a molar mass of 16.00 g/mol.
Molar mass of N2O5 = (2 * 14.01 g/mol) + (5 * 16.00 g/mol)
= 108.01 g/mol
Now, we can calculate the number of moles of N2O5 using the given mass:
Number of moles (n) = Mass / Molar mass
= 3.6 g / 108.01 g/mol
Step 2: Convert the given volume to liters.
The given volume is already in liters.
Now, we can substitute the values into the rate law equation to find the initial rate of decomposition.
Rate = k * [N2O5]
= 5.2 x 10^-3 s^-1 * (3.6 g / 108.01 g/mol) / 0.77 L
Calculating the rate gives us the initial rate of decomposition of N2O5.
To find the initial rate of decomposition of N2O5, we can use the first-order rate law equation:
rate = k * [N2O5]
In this equation, [N2O5] is the concentration of N2O5 at any given time, and k is the rate constant.
To determine the initial rate, we need to know the initial concentration of N2O5. Since we are given the mass of N2O5 and the volume of the container, we can calculate the initial concentration using the equation:
concentration = mass / volume
Let's calculate the initial concentration of N2O5 using the given values:
mass of N2O5 = 3.6 g
volume of container = 0.77 L
concentration = 3.6 g / 0.77 L
concentration ≈ 4.68 g/L
Now we can substitute this value into the rate law equation to find the initial rate:
rate = k * [N2O5]
rate = (5.2 x 10^-3 s^-1) * (4.68 g/L)
Calculating this, we get:
rate ≈ 0.024 s^-1
Therefore, the initial rate of decomposition of N2O5 is approximately 0.024 s^-1.