LAST QUESTION:
When solid NH4NO3 decomposes, a mixture of gases is obtained:
2 NH4NO3(s)--> 4H2O(g) + O2(g) + 2 N2(g)
In an experiment, 5.02 g NH4NO3 decomposes completely in a rigid 5.00-L container. What is the total pressure in the container if the final temperature is 215oC?
Give your answer in atmospheres.
How many mols did yu start with?
That's mols NH4NO3 = grams/molar mass
Now convert mols NH4NO3 to mols H2O using the coefficients in the balanced equation. Do the same for mol O2 and the same for mols N2. Add mols to find total mols, then use PV = nRT to solve for pressure.
To find the total pressure in the container, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature
First, let's find the number of moles of each gas produced in the reaction.
From the balanced equation, we can see that 2 moles of NH4NO3 produce 4 moles of H2O, 1 mole of O2, and 2 moles of N2.
The molar mass of NH4NO3 is:
1(N) + 4(H) + 3(O) = 80.04 g/mol
So, for 5.02 g of NH4NO3, the number of moles can be calculated as:
5.02 g / 80.04 g/mol = 0.0627 mol
According to the balanced equation, for every 2 moles of NH4NO3, 4 moles of H2O, 1 mole of O2, and 2 moles of N2 are produced. Therefore, the moles of gases produced are:
H2O: 0.0627 mol × (4 mol H2O / 2 mol NH4NO3) = 0.1254 mol
O2: 0.0627 mol × (1 mol O2 / 2 mol NH4NO3) = 0.03135 mol
N2: 0.0627 mol × (2 mol N2 / 2 mol NH4NO3) = 0.0627 mol
Now, we can substitute these values into the ideal gas law equation, along with the given volume (5.00 L) and the temperature converted to Kelvin (215°C + 273.15 = 488.15 K):
(0.1254 mol + 0.03135 mol + 0.0627 mol) × R × 488.15 K / 5.00 L = P
Using the value for the ideal gas constant, R = 0.0821 L·atm/(mol·K), we can calculate the pressure:
(0.21945 mol) × 0.0821 L·atm/(mol·K) × 488.15 K / 5.00 L = P
P = 8.603 atm
Therefore, the total pressure in the container is approximately 8.603 atm.
To find the total pressure in the container, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's determine the number of moles of each gas involved in the reaction. Looking at the balanced chemical equation:
2 NH4NO3(s) -> 4H2O(g) + O2(g) + 2N2(g)
We can see that for every 2 moles of NH4NO3, we get 4 moles of water vapor (H2O), 1 mole of oxygen gas (O2), and 2 moles of nitrogen gas (N2).
Given that 5.02 g of NH4NO3 decomposed completely, we can find the number of moles using its molar mass.
Molar mass of NH4NO3:
(N = 14.0067 g/mol, H = 1.00784 g/mol, O = 15.999 g/mol)
NH4NO3 = (14.0067 x 2) + (1.00784 x 4) + (15.999 x 3) = 80.0437 g/mol
Number of moles of NH4NO3:
5.02 g / 80.0437 g/mol = 0.0627 mol NH4NO3
Therefore, we have 0.0627 moles of NH4NO3. Since the stoichiometry in the balanced equation shows that the ratio of NH4NO3 to N2 is 1:2, we have twice as many moles of N2 gas.
Number of moles of N2 gas:
2 x 0.0627 mol = 0.1254 mol N2
Now let's convert the temperature to Kelvin:
Temperature in Kelvin:
215°C + 273.15 = 488.15 K
Finally, we can plug the values into the ideal gas law equation to find the total pressure:
PV = nRT
P(5.00 L) = (0.0627 mol NH4NO3 + 0.1254 mol N2)(0.0821 L atm/mol K)(488.15 K)
Simplifying:
5P = (0.1881 + 0.1031)(40.380115)
5P = (0.2912)(40.380115)
5P = 11.7578
Dividing both sides by 5, we get:
P = 2.35156 atmospheres
Therefore, the total pressure in the container is approximately 2.35156 atmospheres.