Final answer:
The original pressure of 20.0L of compressed gas with final pressure of 560.0 mmHg and volume decreased to 15700mL is 439.60 mmHg, calculated using Boyle's Law.
Step-by-step explanation:
To determine the original pressure of a compressed gas when only the final pressure and volume changes are known, we can use Boyle's Law. This law states that for a given mass of gas at constant temperature, the pressure of the gas times its volume is a constant (P1V1 = P2V2). To find the original pressure (P1), we rearrange the equation to P1 = P2V2/V1.
In this problem, the student has provided the final pressure (P2 = 560.0 mmHg) and the final volume (V2 = 15700 mL), and they need to calculate the original pressure before the volume was decreased from 20.0L.
First, we must convert the original volume from liters to milliliters: 20.0L = 20000 mL (since 1L = 1000 mL). Then we can calculate the original pressure using Boyle's Law.
P1 = (P2 * V2) / V1
= (560.0 mmHg * 15700 mL) / 20000 mL
= 439.60 mmHg
Therefore, the original pressure of the gas was 439.60 mmHg.