Question

a cylinder with a moveable piston contains 0.553 mol of gas and has a volume of 253 ml. what is its volume if has 0.365 mol of gas in the cylinder. (assume constant temperature and pressure.)

Answer 1

V = 0.167L

Step-by-step explanation:

We can use the ideal gas law:

PV = nRT

where P, V, and T are pressure, volume, and temperature (Kelvin only). R is the gas constant and n is the moles of gas.

We want the volume of gas when the moles changes. Let's set up two equations, 1 for each state. Since both temperature and pressure are constant, we can simply use the terms P and T both states.

Initial (0.553 moles and 253 ml)): P*(0.253L) = (0.553 moles)RT

Second (0.365 moles, unknown volume, V): P*V = (0.365 moles)RT

P*(0.253L) = (0.553 moles)RT

P*V = (0.365 moles)RT

Lets set these up as a ratio:

P*(0.253L)/P*V = ((0.553 moles)RT)/((0.365 moles)RT)

P, T and R all cancel to 1, and the moles unit cancels:

(0.253L)/V = (0.553)/((0.365)

The ratio of the volumes is in direct proportion with the ratio of the moles.

Rearrange and solve:

(0.253L) = (0.553)/((0.365)V

(0.253L)*(0.365/0.553) = V

V = 0.167L