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Chapter 33: Problem 3

How does the volume of a gas (at constant \(T\) and \(P\) ) change as the number of molecules is increased?

Short Answer

Expert verified
The volume of a gas increases proportionally as the number of molecules is increased, while keeping temperature and pressure constant.

Step by step solution

01

Understand the Ideal Gas Law

The Ideal Gas Law is given by the formula \(PV = nRT\), where \(P\) represents pressure, \(V\) represents volume, \(n\) represents the number of moles, \(R\) is the ideal gas constant, and \(T\) is the absolute temperature.
02

Isolate the Required Variables

Given that the pressure (\(P\)) and temperature (\(T\)) are constant, the formula becomes \(V = nRT/P\). The right-hand part of the equation, \(RT/P\), can be seen as a constant \(\kappa\) (because \(R\), \(T\) and \(P\) are all constant in this case), so the formula simplifies into \(V = n\kappa\).
03

Determine the Relationship

From the simplified equation \(V = n\kappa\), it's clear that \(V\) and \(n\) have a direct proportional relationship – as \(n\), the number of molecules, increases, the volume \(V\) of the gas also increases, assuming the temperature and pressure are kept constant.

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Most popular questions from this chapter

How does the volume of a gas (at constant \(n\) and \(T\) ) change as the pressure is increased?

How does the volume of a gas (at constant \(n\) and \(P\) ) change as the temperature is raised?

For each case, rearrange the Ideal Gas Law Equation to show that it is consistent with the given law or hypothesis and obtain an expression for the corresponding constant. a) Boyle's Law, \(\mathrm{k}_{\mathrm{B}}\) b) Charles' Law, \(\mathrm{k}_{\mathrm{C}}\) c) Avogadro's Hypothesis, \(\mathrm{k}_{\mathrm{A}}\)
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