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A gas storage cylinder in an ordinary chemical laboratory measures 4.4 cm wide and 17.cm high. This is the label on it.Contents: N2 gasPressure: 29.8 atmIf 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. Round your answer to 2 significant digits.

Respuesta :

Explanation:

We assume equal number of moles at constant temperature. Therefore,  

                        [tex]P_{1}V_{1} = P_{2}V_{2}[/tex]

Hence,

                  [tex]V_{2} = V_{1} \times \frac{P_{1}}{P_{2}}[/tex]

where,    [tex]P_{2}[/tex] = atmospheric pressure = 1 atm

               [tex]V_{2}[/tex] = volume bag + volume gas left over in cylinder.

Also we know that formula for volume of cylinder is as follows,

                            V = [tex]\pi r^{2}h[/tex]

It is given here that, diameter of cylinder = 4.4 cm

Therefore, radius = [tex]\frac{4.4}{2}[/tex]

                             = 2.2 cm

and, h =17 cm

Hence, calculate value of [tex]V_{2}[/tex] as follows.

        [tex]V_{2} = 3.1415 \times (2.2)^{2} \times 17 \times (\frac{1 L}{1000} cm^{3}) \times (\frac{29.8}{1 atm})[/tex]

                          = 7.7 L

Thus, we can conclude that final volume of nitrogen gas, including what's collected in the plastic bag and what's left over in the cylinder is 7.7 L.

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