Anonymous
Anonymous asked in Science & MathematicsChemistry · 1 year ago

# Chemistry Question?

When ammonium nitrate (NH4NO3) explodes, all the products are gases:

2 NH4NO3s→4 H2Og+O2g+2 N2g

If 5.00 g of NH4NO3 explodes in a closed 2.00 L container that originally contains air at p=1.00 bar and T=25°C, and the temperature rises to 205°C, what total pressure develops?

The answer is 5.89 bar. Can someone explained the steps in detail?

Relevance

Ignoring the volume of the solid NH4NO3 before it decomposes:

Notice that the balanced equation shows that a total of 4 + 1 + 2 = 7 moles of various gases are produced by each 2 moles of NH4NO3 that decompose.

(1.00 bar) x (205 + 273) K / (25 + 273) K = 1.604 bars air

(5.00 g NH4NO3) / (80.0434 g NH4NO3/mol) x (7 mol gases / 2 mol NH4NO3) =

0.21863 mol gases produced

P = nRT / V = (0.21863 mol) x (0.083144598 L bar/K mol) x (205 + 273) K / (2.00 L) =

4.345 bars of decomposition product gases

1.604 bars + 4.345 bars = 5.95 bars total

• concepts

.. PV = nRT

.. where n = total moles gas = moles air initial + moles gas formed

.. note from the balanced equation, 2 mol NH4NO3 ---> 7 mol gas

via ideal gas law... moles air initial

.. PV = nRT

.. .. n = PV/(RT) = (1.00bar * 1atm/1.01325bar) * (2.00L) / ((0.08206 Latm/molK) * (298.15K))

.. .. n air = 0.0807 mol

via dimensional analysis... moles gas produced

.. 5.00g NH4NO3.. .. .1 mol NH4NO3.. ... .. ..7 mol gas

---- ---- ---- --- ---- x ----- ---- ---- ----- --- x ---- ---- ---- --- ---- = 0.2186 mol gas

.. .. ... .. .1. ... ... .. . .80.04g NH4NO3.. ... 2 mol NH4NO3

then

.. PV = nRT

.. P = nRT/V

.. P = (0..2186mol + 0.0807mol) * (0.08206 Latm/molK) * (478.15K) / (2.00L) * (1.01325bar/1atm)

.. P = 5.94bar

do check my calcs!

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