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Ammonium nitrate decomposes explosively upon heating according to the balanced equation: 2NH4NO3(s)→2N2(g) O2(g) 4H2O(g) Part A Calculate the total volume of gas (at 24 âC and 749 mmHg ) produced by the complete decomposition of 1.56 kg of ammonium nitrate.

Respuesta :

kenmyna

 the total volume  of   gas is 1687.75 L

Calculation

2NH4NO3→ 2N2(g) +O2(g) + 4 H2O(g)

Volume of a gas is calculated using ideal gas equation

that is Pv=nRT

P(pressure)= 749 mm Hg

V(volume)=?

n (no of moles)

to  calculate the  number  of  moles  of  gas.

  find  the  moles of NH4NO3

  moles=mass/molar  mass

  mass=1.56 kg = 1.56 x 1000 = 1560 g

 molar mass of NH4NO3 =14+(1 x4) + 14 +( 16  x3) = 80 g/mol

moles= 1560 g/80 g/mol=19.5 moles

by use of mole ratio of NH4NO3 : total number of  mole of a gas  from equation above  which is = 2:7 therefore the moles of gas = 19.5 x7/2 =68.25 moles

therefore n=68.35 mole

R( gas  constant)  =62.36367  L.mmhg/mol.K

T(temperature) =24°c into k = 24 +273=297K

by  making V the subject of the formula

v=nRT/P

V= (68.25  mol  x 62.36367 L.mmhg/mol.k  x 297 k) / 749  mmhg = 1687.75 L

Eduard22sly

The total volume of gas (at 24 °C and 749 mmHg) produced by the complete decomposition of 1.56 Kg of ammonium nitrate, NH₄NO₃ is 1687.74 L

How to determine the mole of NH₄NO₃

  • Mass of NH₄NO₃ = 1.56 Kg = 1.56 × 1000 = 1560 g
  • Molar mass of NH₄NO₃ = 80 g/mol
  • Mole of NH₄NO₃ =?

Mole = mass / molar mass

Mole of NH₄NO₃ = 1560 / 80

Mole of NH₄NO₃ = 19.5 moles

How to determine the total moles of the gas produced

2NH₄NO₃(s) —> 2N₂(g) + O₂(g) + 4H₂O(g)

From the balanced equation above

  • Mole of N₂ = 2 moles
  • Mole of O₂ = 1 mole
  • Mole of H₂O = 4 moles
  • Total mole = 2 + 1 + 4 = 7 moles

From the balanced equation above,

2 moles of NH₄NO₃ produced 7 moles of gas.

Therefore,

19.5 moles of NH₄NO₃ will react to produce = (19.5 × 7) / 2 = 68.25 moles of gas

How to determine the total volume of gas

  • Temperature (T) = 24 °C = 24 + 273 = 297 K
  • Pressure (P) = 749 mmHg  
  • Gas constant (R) = 62.363 mmHg.L/Kmol
  • Number of mole (n) = 68.25 moles
  • Volume (V) =?

The volume of the gas can be obtained by using the ideal gas equation as follow:

PV = nRT

Divide both side by P

V = nRT / P

V = (68.25 × 62.363 × 297) / 749

V = 1687.74 L

Learn more about ideal gas equation:

https://brainly.com/question/4147359

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