Two moles of an ideal gas originally at 380 torr and 298 K are compressed at constant temperature to a final pressure of 680 torr. Use the ideal gas law to calculate the volumes of gas at the initial and final pressures.(3pts)Initial volume (L), at 380 torr

To solve this problem, we will use the ideal gas law, which is PV = nRT.

Step 1: Convert the pressures from torr to atm because R (ideal gas constant) is usually defined with pressure in atm. 1 atm = 760 torr. So, 380 torr = 380/760 = 0.5 atm and 680 torr = 680/760 = 0.895 atm.

Step 2: Calculate the initial volume. We know the number of moles (n) = 2, R = 0.0821 L.atm/(mol.K), T = 298 K, and P = 0.5 atm. Substituting these values into the ideal gas law gives us V = nRT/P = (2 mol * 0.0821 L.atm/(mol.K) * 298 K) / 0.5 atm = 48.2 L.

Step 3: Calculate the final volume. The temperature and the number of moles remain the same, but the pressure is now 0.895 atm. Substituting these values into the ideal gas law gives us V = nRT/P = (2 mol * 0.0821 L.atm/(mol.K) * 298 K) / 0.895 atm = 27.3 L.

So, the initial volume of the gas is 48.2 L and the final volume is 27.3 L.