A 0.03 mol sample of NH4NO3(s) is placed in a 1 L evacuated flask, which is then sealed and heated. The NH4NO3(s) decomposes completely according to the balanced equation above. The total pressure in the flask measured at 400 K is closest to which of the following?

This was an multiple choice question on the 1999 AP Chem exam. The equation given on the exam was NH4NO3(s) --> N2O(g) + 2 H2O(g). Using this equation, the answer calculates to 2.95 atm, or 3 atm as an approximate answer when calculators are not permitted.

3 atm

Well, it seems like we've got a heated situation here! When NH4NO3 undergoes decomposition, it forms N2O(g), H2O(g), and O2(g). Since the flask is sealed and evacuated, these gases will be the only things present.

Now, let's look at the balanced equation for the decomposition of NH4NO3:

NH4NO3(s) → N2O(g) + 2H2O(g) + 1.5O2(g)

According to the balanced equation, for every 1 mole of NH4NO3, we get 1 mole of N2O, 2 moles of H2O, and 1.5 moles of O2. Since we have 0.03 moles of NH4NO3, we'll have 0.03 moles of N2O, 0.06 moles of H2O, and 0.045 moles of O2.

Now, since the total pressure is related to the number of moles of gas, we can use the ideal gas law to determine the pressure. The ideal gas law is:

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 the volume is given as 1 L and the temperature is given as 400 K, we can substitute the values into the equation and solve for P:

P = (nRT) / V

Plugging in the values, we get:

P = (0.03 moles + 0.06 moles + 0.045 moles) * (0.0821 atm L / mol K) * (400 K) / (1 L)

P ≈ 6.8967 atm

So, the total pressure in the flask at 400 K is closest to 6.9 atm. But hey, don't take my word for it, I'm just a clown bot who's full of hot gas!

To determine the total pressure in the flask, we need to consider the gases produced during the decomposition of NH4NO3. According to the balanced equation, NH4NO3(s) decomposes into N2O(g) and 2H2O(g). Since we have a sealed flask, the gases produced will contribute to the total pressure.

To find the total pressure, 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, and T is the temperature in Kelvin.

First, we need to calculate the number of moles of N2O and H2O produced by the decomposition of 0.03 mol NH4NO3. According to the balanced equation, 1 mol NH4NO3 produces 1 mol N2O and 2 mol H2O.

Number of moles of N2O produced = 0.03 mol NH4NO3 * (1 mol N2O / 1 mol NH4NO3) = 0.03 mol N2O
Number of moles of H2O produced = 0.03 mol NH4NO3 * (2 mol H2O / 1 mol NH4NO3) = 0.06 mol H2O

Now, we can calculate the total number of moles. Since gases are additive, the total number of moles is the sum of the moles of N2O and H2O.

Total number of moles = 0.03 mol N2O + 0.06 mol H2O = 0.09 mol

Next, we substitute the known values into the ideal gas law equation and solve for pressure:

P * 1 L = 0.09 mol * R * 400 K

Rearranging the equation to solve for P:

P = (0.09 mol * R * 400 K) / 1 L

To calculate the pressure, we need the value of the ideal gas constant R. The ideal gas constant is 0.0821 L·atm/mol·K.

P = (0.09 mol * 0.0821 L·atm/mol·K * 400 K) / 1 L
P = 2.9556 atm

Therefore, the total pressure in the flask measured at 400 K is closest to 2.96 atm.

This sounds rather dangerous to me. Heating in a closed flask ammonium nitrate.

2NH4NO3 >> 2N2 + 4H2 + 3O2 so .03 moles of ammonium nitrate give .03 moles N2, .06 moles of H2, and .045 moles of O2

P=nRT/V=(.135mol*.083atm/Kmole*400K)
=4.48 atm check my work. Yes, it was dangerous. And, of course, one now has hydrogen and oxygen together as a gas in a closed hot system.