Question

compressibility factor Z for N2 at -23 degree Celsius and 25 ATM pressure each 1. 2 .calculate moles of N2 gas required to fill a gas cylinder of 7 litre capacity under the given given conditions (use R=1/12 Latmmol-1 K-1)​

Answer 1

7 moles of N₂ gas are required to fill the gas cylinder.

Explanation:

Given:

• Compressibility factor (Z) = 1.2
• The Pressure of N₂ gas = 25 atm
• Temperature = -23°C = 250.15 K
• Gas constant (R) = $\frac{1}{12}$ l atm mol⁻¹ K⁻¹
• Volume of the gas cylinder (V) =  7 l

To find:

• The number of moles of N₂ gas required to fill the gas cylinder (n).

Solution:

The formula for compressibility factor is:

• $Z=\frac{PV}{nRT}$

On rearranging the formula, we get:

• $n=\frac{PV}{ZRT}$

Substitute the values in the above formula:

• $n=\frac{25\times7}{1.2\times\frac{1}{12}\times250.15 }$

• $n=6.996 moles\\or\\n=7 moles$

Therefore, 7 moles of N₂ gas are required to fill the gas cylinder.