A sample of an ideal gas occupies volume at absolute temperature while the pressure…

CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance

Problem

A sample of an ideal gas occupies volume

V_1

at absolute temperature

T_1

while the pressure is kept constant. (i) Starting from the fundamental relation between volume and temperature at constant pressure, derive the linear equation that connects

V

and

T

for this gas. (ii) Hence show that the slope of the

V

–

T

graph is

\dfrac{V_1}{T_1}

. (iii) For a gas that has

V_1 = 250\,\text{cm}^3

T_1 = 300\,\text{K}

, calculate the numerical value of the slope and use it to find the volume at

T = 450\,\text{K}

. (iv) Using your derived relation, find the absolute temperature at which the volume will reach

400\,\text{cm}^3

for this gas under the same pressure.

Related theory

Gaseous State
States of Matter
Dimensional analysis
Some Basic Concepts of Chemistry
Charles' law
Gay Lussac's Law of Gaseous Volumes
Ideal Gas Law
Ideal gas equation

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