Question

How many moles of oxygen are lost in the following problem?

A cylinder with a moveable piston records a volume of 12.7 L when 3.5 mol of oxygen is added. The gas in the cylinder has a pressure of 5.83 atm. The cylinder develops a leak, and the volume of the gas is now recorded to be 12.1 L at the same pressure.

Answer 1

.16 moles of Oxygen assuming the temperature is at standard temperature.

Explanation:

Use Boyles Law to find the volume of Oxygen lost at standard pressure of 1 atm.

`P_1 xx V_1 = P_2 xx V_2`

`P_1 = 5.83`
`V_1 = 0.6`
`P_2 = 1.00`
`V_2` = Volume of Oxygen lost.

Solving the problem to find the Volume of Oxygen lost

`5.83 xx 0.6 = 1 xx V_2`

3.50 liters = `V_2`

22.4 liters = 1 mole at STP for an ideal gas.

Assuming Oxygen is close to an ideal gas

`3.50/22.4` = moles Oxygen.

0.156 = moles of Oxygen.

Answer 2

The cylinder has lost 0.2 mol of oxygen.

Explanation:

The pressure and temperature are constant.

Only the volume and the number of moles are changing.

The appropriate relationship is therefore Avogadro's law: the volume of a gas is directly proportional to the number of moles, if all other variables are held constant.

In symbols,

`V ∝ n`

`V = kn` or `V/n = k`

This leads to the relation

`color(blue)(bar(ul(|color(white)(a/a) V_1/n_1 = V_2/n_2color(white)(a/a)|)))" "`

In this problem,

`V_1 = "12.7 L"; n_1 = "3.5 mol"`
`V_2 = "12.1 L"; n_2 = "?"`

`n_2 = n_1 × V_2/V_1 = "3.5 mol" × (12.1 color(red)(cancel(color(black)("L"))))/(12.7 color(red)(cancel(color(black)("L")))) = "3.33 mol"`

`Δn = n_2 - n_1 = "3.33 mol - 3.5 mol" = "-0.2 mol"` (1 significant figure)