What volume of N2O (s) will be generated if 3.13 g of NH4NO3 (s) decomposes at 1.00 atm and 50 degrees celsius, given the following decomposition reaction: NH4NO3 (s) --> N2O (g) + 2 H2) (l)?
To determine the volume of N2O gas generated, we need to follow these steps:
Step 1: Convert the mass of NH4NO3 to moles.
To do this, we need the molar mass of NH4NO3, which can be calculated by adding up the molar masses of its constituent elements.
Molar mass of NH4NO3 = (1 * molar mass of N) + (4 * molar mass of H) + molar mass of O
The molar masses of N, H, and O are approximately 14 g/mol, 1 g/mol, and 16 g/mol, respectively.
Substituting the values, we get:
Molar mass of NH4NO3 = (1 * 14 g/mol) + (4 * 1 g/mol) + 3 * 16 g/mol
Molar mass of NH4NO3 = 80 g/mol
Now we can convert the mass of NH4NO3 to moles using the formula:
Moles of NH4NO3 = Mass of NH4NO3 / Molar mass of NH4NO3
Plugging in the values, we have:
Moles of NH4NO3 = 3.13 g / 80 g/mol
Moles of NH4NO3 ≈ 0.039 moles
Step 2: Use the balanced equation to find the stoichiometry between NH4NO3 and N2O.
From the balanced equation, we can determine that 1 mole of NH4NO3 produces 1 mole of N2O gas.
Therefore, moles of N2O = Moles of NH4NO3 ≈ 0.039 moles
Step 3: Apply the Ideal Gas Law to find the volume of N2O.
The Ideal Gas Law provides the relationship between pressure (P), volume (V), moles of gas (n), and temperature (T). The formula is:
PV = nRT
We are given the pressure (P = 1.00 atm), temperature (T = 50°C = 50 + 273.15 = 323.15 K), and the moles of N2O (n = 0.039 moles).
We also need to know the ideal gas constant (R), which is equal to 0.08206 L·atm/(mol·K).
Rearranging the Ideal Gas Law to solve for volume (V), we get:
V = (nRT) / P
Substituting the values, we have:
V = (0.039 moles * 0.08206 L·atm/(mol·K)) * 323.15 K / 1.00 atm
Calculating this expression will give us the volume of N2O in liters.
Here is how you work a stoichiometry problem.
1. Write and balance the equation. You have that.
2. Convert what you have (in this case grams NH4NO3) to mols. mols = grams/molar mass = ?
3. Using the coefficients in the balanced equation, convert mols of what you have to mols of what you want(in this case N2O).
mols N2O = ?mols NH4NO3 x (1 mol N2O/1 mol NH4NO3) = ?
4. Now convert mols N2O at the conditions listed with PV = nRT.
(NOTE: If you wanted grams N2O instead it would be grams N2O = mols N2) x molar mass N2O = ?
Print this out. It will work all of your stoichiometry problems. It's just a four step process.