A cylinder, with a piston pressing down with a constant pressure, is filled with 2.10 moles of a gas (n1), and its volume is 50.0 L (V1). If 0.300 mole of gas leak out, and the pressure and temperature remain the same, what is the final volume of the gas inside the cylinder?

42.86 L

Explanation:

The following data were obtained from the question:

Initial mole (n1) = 2.10 moles

Initial volume (V1) = 50.0 L

Final mole (n2) = 2.10 – 0.3 = 1.8 mole

Final volume (V2)

From the ideal gas equation:

PV = nRT

Divide both side by P

V = nRT/P

Divide both side n

V/n = RT/P

Since the pressure (P) and temperature (T) are constant, therefore,

V/n = constant

V1/n1 = V2/n2

V1 is the initial volume = 50L

n1 is the initial mole = 2.1 moles

V2 is final volume =.?

n2 is the final mole = 1.8 mole

V1/n1 = V2/n2

50/2.1 = V2/1.8

Cross multiply to express in linear form

2.1 x V2 = 50 x 1.8

Divide both side by 2.1

V2 = (50 x 1.8)/2.1

V2 = 42.86 L

Therefore, the final volume of the gas is 42.86 L

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