An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27°C. The mass of the oxygen withdrawn from the cylinder is nearly equal to:

[Given, R=100/12 J mol^-1 k^-1 and molecular mass of O₂ = 32, 1 atm pressure = 1.01 × 10⁵ N/m]

To find the mass of oxygen withdrawn from the cylinder, we first need to determine the number of moles of oxygen remaining in the cylinder after some of it has been withdrawn.

Let the initial state of the oxygen in the cylinder be represented by:
Initial volume, $V=30\text{litres}=30\times {10}^{-3}{\text{m}}^3$
Initial number of moles, $n_1=18.20\text{moles}$

After some oxygen is withdrawn, the gauge pressure drops to 11 atm. The pressure inside the cylinder is the absolute pressure, which is the sum of gauge pressure and atmospheric pressure:
Absolute pressure, $P=P_{\text{gauge}}+P_{\text{atm}}=11\text{atm}+1\text{atm}=12\text{atm}$

Given that $1\text{atm}=1.01\times {10}^5{\text{N/m}}^2$, the final absolute pressure in SI units is:
$P=12\times 1.01\times {10}^5{\text{N/m}}^2=12.12\times {10}^5{\text{N/m}}^2$

The final temperature is $T={27}^{\circ }\text{C}=27+273=300\text{K}$.
The gas constant is given as $R=\frac{100}{12}{\text{J mol}}^{-1}{\text{K}}^{-1}$.

Using the ideal gas equation, $PV=n_{2}RT$, where $n_2$ is the final number of moles of oxygen remaining in the cylinder:
$n_2=\frac{PV}{RT}$

Substituting the given values:
$n_2=\frac{(12.12\times {10}^5)\times (30\times {10}^{-3})}{\left(\frac{100}{12}\right)\times 300}$
$n_2=\frac{12.12\times 30\times {10}^2}{\frac{100}{12}\times 300}$
$n_2=\frac{363600}{2500}=14.544\text{moles}$

The number of moles of oxygen withdrawn from the cylinder is:
$\Delta n=n_1-n_2=18.20-14.544=3.656\text{moles}$

The molecular mass of ${\text{O}}_2$ is $32\text{g/mol}=32\times {10}^{-3}\text{kg/mol}$.
The mass of oxygen withdrawn is:
$m=\Delta n\times M=3.656\times 32\times {10}^{-3}\text{kg}$
$m\approx 0.11699\text{kg}\approx 0.116\text{kg}$

Therefore, the mass of the oxygen withdrawn is nearly equal to 0.116 kg.