# Gas Laws: Calculations using Boyle's Law

## Concepts

Boyle's Law states that the product of the pressure and volume for a gas is a constant, provided the amount of gas (moles n) and the temperature (T) remain constant. Written in mathematical terms, this law is

P V = constant

A common use of this law is to predict how a change in pressure will alter the volume of the gas or vice versa, for constant n and T. Such a problem can be regarded as a two state problem: the initial state (represented by subscript i on variables) and the final state (represented by subscript f on variables). If a sample of gas initially at pressure Pi and volume Vi is subjected to a change that does not change the amount of gas or the temperature, the final pressure Pf and volume Vf are related to the initial values by the equation

Pi Vi   =   Pf Vf   =   constant

## Experiment Background

### Objective

• Use Boyle's Law to predict the final pressure for a gas that has undergone an expansion.

In both parts of this exercise, you will work with two glass bulbs connected by a tube with a stopcock. Initially, the bulb on the right is completely evacuated (that is, it contains no gas and has a pressure of zero) while the bulb on the left contains a sample of gas at pressure Pi. A manometer is provided to measure the pressure in the left bulb.

When the stopcock is opened, the gas in the left bulb will expand to occupy both bulbs and the pressure in the left bulb will change accordingly. The temperature of the system is held constant throughout the experiment. No gas can enter or leave the set of bulbs, thus the moles of gas is also constant.

Information on the volumes of the two bulbs will be given to you, and you may read the initial pressure from the manometer. Use Boyle's Law to calculate the final pressure. Then open the stopcock and see if your prediction is correct.

## Experiment

Each time you press the "New Conditions" button, the experiment will be reset with new volumes for the two bulbs and a new initial pressure. After calculating the final pressure, press the "Open Stopcock" button to allow the gas to expand and check your prediction.

Practice the calculations until you are able to solve the problem consistently. Bear in mind that the final volume, Vf , is the sum of the volumes of the two bulbs.

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