What volume of nitrogen gas at 1 atm would be required to fill a 3 liter tank to 1800 psi? Assume that no temperature change occurs during the compression.

Question

Quizplus · Accepted Answer

To solve this problem, we use the ideal gas law in the form $P_1V_1 = P_2V_2$, where $P_1$ and $V_1$ are the initial pressure and volume, and $P_2$ and $V_2$ are the final pressure and volume. Given that the final pressure $P_2$ is 1800 psi and we want to fill a 3-liter tank, we need to convert the pressure to atm (since 1 atm = 14.7 psi) and the volume to the same units for consistency. First, convert 1800 psi to atm:$$1800 \, \text{psi} \times \frac{1 \, \text{atm}}{14.7 \, \text{psi}} \approx 122.45 \, \text{atm}$$Since no temperature change occurs, we can assume $P_1 = 1 \, \text{atm}$ and $V_1$ is what we're solving for. $P_2 = 122.45 \, \text{atm}$ and $V_2 = 3 \, \text{liters}$.Rearrange the ideal gas law to solve for $V_1$:$$V_1 = \frac{P_2V_2}{P_1} = \frac{122.45 \, \text{atm} \times 3 \, \text{liters}}{1 \, \text{atm}} = 367.35 \, \text{liters}$$Therefore, the volume of nitrogen gas at 1 atm required to fill a 3-liter tank to 1800 psi is approximately 367 liters.

What Volume of Nitrogen Gas at 1 Atm Would Be