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

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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.

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.

##### 2 Answers

#### Answer:

.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.

Solving the problem to find the Volume of Oxygen lost

3.50 liters =

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

Assuming Oxygen is close to an ideal gas

0.156 = moles of Oxygen.

#### Answer:

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,

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,