Question

A cylinder, with a piston pressing down with a constant pressure, is filled with 1.90 moles of a gas (n1), and its volume is 49.0 L (V1). If 0.500 mole of gas leak out, and the pressure and temperature remain the same, what is the final volume of the gas inside the cylinder? Express your answer with the appropriate unit

Answer 1

the final volume of the gas inside the cylinder after 0.500 mole has leaked out is 37.0 L.

Step-by-step explanation:

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Since the pressure and temperature are constant, we can assume that they remain constant during the process of the gas leaking out. So, the initial state (1) and the final state (2) of the gas can be described as follows:

(1) PV1 = n1RT

(2) PV2 = (n1 - 0.500)RT

Now, we can find the final volume of the gas by substituting the known values into the equation and solving for V2:

V2 = (n1RT)/P = (1.90 * 8.31 * T)/P

V2 = (1.90 * 8.31 * T)/P = (1.90 * 8.31 * T)/P = 49.0

V2 = 49.0 L * (1.90 - 0.500) / 1.90

V2 = 37.0 L