Question

2. An almost empty natural gas storage tank contains 2.65 kg of methane gas at 650.5 kPa
and 18.0°C. What is the volume of the storage tank?

Answer 1

Considering the ideal gas law, the volume of the storage tank is 615.5987 L.

Ideal gas law

An ideal gas is a theoretical gas that is considered to be composed of randomly moving point particles that do not interact with each other. Gases in general are ideal when they are at high temperatures and low pressures.

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.  

Volume of the storage tank

In this case, you know:

• P= 650.5 kPa= 6.42 atm (being 101.325 kPa= 1 atm)
• V= ?
• T= 18 °C= 291 K (being 0 C= 273 K)
• R= 0.082 $\frac{atmL}{molK}$

• n= 2.65 kg=  2650 g× $\frac{1 mole}{16 gramos}$= 165.625 moles (being 16 $\frac{g}{mole}$ the molar mass of the methane)

Replacing in the ideal gas law:

6.42 atm× V = 165.625 moles ×0.082 $\frac{atmL}{molK}$× 291 K

Solving:

V= $\frac{165.625 moles x0.082 \frac{atmL}{molK}x291 K}{6.42 atm}$

V= 615.5987 L

Finally, the volume of the storage tank is 615.5987 L.

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