Considering the ideal gas law, 392.2 L of gas would be formed at 500 ∘C and 1.00 atm pressure by explosion of 495 g of NH₄NO₃.
Ideal gases are a simplification of real gases that is done to study them more easily. It is considered to be formed by point particles, do not interact with each other and move randomly. It is also considered that the molecules of an ideal gas, in themselves, do not occupy any volume.
The pressure, P, the temperature, T, and the volume, V, of an ideal gas, are related by a simple formula called the ideal gas law:
P×V = n×R×T
Where:
P is the gas pressure.
V is the volume that occupies.
T is its temperature.
R is the ideal gas constant. The universal constant of ideal gases R has the same value for all gaseous substances.
n is the number of moles of the gas.
In this case, you know:
- P= 1 atm
- V = ?
- n= 495 g÷ 80 g/mol= 6.1875 moles
- R= 0.082 atmL/molK
- T= 500 °C= 773 K (being 0°C= 273 K)
Replacing in the ideal gas law:
1 atm×V = 6.1875 moles×0.082 atmL/molK× 773 K
Solving:
V = [6.1875 moles×0.082 atmL/molK× 773 K]÷ 1 atm
V= 392.2 L
Finally, 392.2 L of gas would be formed at 500 ∘C and 1.00 atm pressure by explosion of 495 g of NH₄NO₃.