a gas storage cylinder in an ordinary chemical laboratory measures 7.6 cm wide and 30. cm high. this is the…

a gas storage cylinder in an ordinary chemical laboratory measures 7.6 cm wide and 30. cm high. this is the label on it. contents: n₂ gas pressure: 12.4 atm 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 whats collected in the plastic bag and whats left over in the cylinder? write your answer in liters. be sure your answer has the correct number of significant digits.

a gas storage cylinder in an ordinary chemical laboratory measures 7.6 cm wide and 30. cm high. this is the label on it. contents: n₂ gas pressure: 12.4 atm 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 whats collected in the plastic bag and whats left over in the cylinder? write your answer in liters. be sure your answer has the correct number of significant digits.

Answer

Explanation:

Step1: Calculate initial volume of cylinder

The cylinder is a cylinder - shaped container. The volume formula for a cylinder is $V = \pi r^{2}h$. The diameter $d = 7.6$ cm, so the radius $r=\frac{d}{2}=\frac{7.6}{2}=3.8$ cm and $h = 30$ cm. Then $V_{1}=\pi\times(3.8)^{2}\times30\ cm^{3}\approx1362.46\ cm^{3}$. Convert to liters: $V_{1}=1362.46\ cm^{3}\times\frac{1\ L}{1000\ cm^{3}} = 1.36246\ L$.

Step2: Use Boyle's law

Boyle's law is $P_{1}V_{1}=P_{2}V_{2}$. The initial pressure $P_{1}=12.4$ atm, the initial volume $V_{1}=1.36246$ L, and the final pressure $P_{2} = 1$ atm (atmospheric pressure). We need to solve for $V_{2}$. Rearranging Boyle's law gives $V_{2}=\frac{P_{1}V_{1}}{P_{2}}$. Substitute the values: $V_{2}=\frac{12.4\ atm\times1.36246\ L}{1\ atm}=16.9\ L$ (rounded to 3 significant digits).

Answer:

$16.9$ L