Question

A gas storage cylinder in an ordinary chemical laboratory measures 4.6 cm wide and 18. cm high.This is the label on it.Contents: N₂ gasPressure: 28.2 atmIf the cylinder is opened and the gas allowed to escape into a large empty plastic bag, what will be the final volume ofnitrogen 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.X5 ?EFindAr100

Answer 1

`8.5\text{ L}`

Step-by-step explanation:

According to Boyles' law, the volume of a given mass of gas is inversely proportional to its pressure

Mathematically:

`\begin{gathered} P_1V_1\text{ = P}_2V_2 \\ V_2\text{ = }(P_1V_1)/(P_2) \end{gathered}`

Where:

P1 is the initial pressure which is 28.2 atm

V1 is the volume of the cylinder which is:

`\begin{gathered} V_1\text{ = }\pi* r^2* h \\ r\text{ = radius = }(4.6)/(2)\text{ = 2.3 cm} \\ h\text{ = 18 cm} \\ \\ V_1\text{ = }\pi*2.3^2*18\text{ = 299.14 cm}^3 \end{gathered}`

We convert V1 to liters by multiplying by 0.001 L

That would be:

`299.14\text{ }*\text{ 0.001 = 0.3 L}`

P2 is the atmospheric pressure which is 1 atm

Substituting the values, we have:

`V_2\text{ = }\frac{28.2\text{ }*0.3}{1}\text{ = 8.46 L}`