Chapter 5, Problem 5.108QP

Interpretation Introduction

Interpretation:

The volume of gas contained in a steel bottle at STP has to be calculated

Concept Introduction:

Combined Gas Law:

Boyle’s law:

$\text{ V}\alpha \frac{1}{\text{P}}\text{ (at constant T)}$

$P_f{V}_f=P_i{\text{V}}_i\text{ (at constant T)}$

Charles’s law:

$\text{ V}\alpha \text{ T (at constant P)}$

$\frac{V_f}{T_f}=\frac{V_i}{T_i}\text{ (at constant P)}$

The boyle’s law and charles’s law is combined and stated as “the volume (V) of a given gas is directly proportional to temperature (T) and inversely proportional to pressure (P)”

$\text{ V}\alpha \frac{\text{T}}{\text{P}}$

For a sample of gas supposing a change in temperature, volume and pressure, the combined gas law can be written as

$\frac{P_f{V}_f}{T_f}=\frac{P_i{V}_i}{T_i}$

On rearranging, we get

$V_f=V_i\times \frac{P_i}{P_f}\times \frac{T_f}{T_i}$

Where,

$T_{i}and{\text{ T}}_f$ are initial temperature  and final temperature respectively

$V_{i}and{\text{ V}}_f$ are initial volume and final volume respectively

$P_{i}and{\text{ P}}_f$ are initial pressure  and final pressure respectively