A gas storage cylinder in an ordinary chemical laboratory measures 2.5cm wide and 10.cm high.This is the label on it. Contents: N2 gas  Pressure: 22.6atm   If the cylinder is opened and the gas allowed to escape into a large empty plastic bag, what will be the final volume of nitrogen gas, including what's collected in the plastic bag and what's left over in the cylinder? Write your answer in liters. Be sure your answer has the correct number of significant digits.

To solve this problem, we need to use the ideal gas law, which states that the pressure of a gas times its volume is equal to the number of moles of the gas times the gas constant times the temperature (PV=nRT). However, in this case, we are not given the temperature or the number of moles of gas, so we need to make some assumptions.

First, let's assume that the temperature is at standard room temperature, which is approximately 298K.

Second, we can calculate the volume of the cylinder using the formula for the volume of a cylinder, which is V=πr²h. The radius of the cylinder is half of the diameter, so r=1.25cm. The height of the cylinder is 10cm. So, the volume of the cylinder is V=π(1.25cm)²(10cm)=49.1cm³.

Next, we need to convert this volume to liters, since the question asks for the answer in liters. There are 1000cm³ in a liter, so the volume of the cylinder is 49.1cm³*(1L/1000cm³)=0.0491L.

Now, we can use the ideal gas law to calculate the volume of the gas at standard pressure (1atm). The pressure of the gas in the cylinder is 22.6atm, so the volume of the gas at standard pressure is V=(22.6atm/1atm)*0.0491L=1.11L.

Therefore, the final volume of the nitrogen gas, including what's collected in the plastic bag and what's left over in the cylinder, is 1.11L.