Question

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

Short answer

With temperature and pressure constant, the volume of a gas increases proportionally as the number of molecules increases.

Step-by-step solution

Identify the given constants

The problem specifies that both the temperature \(T\) and pressure \(P\) are constant. Neither \(T\) nor \(P\) will change throughout the problem.

Observe the Expression

Consider the ideal gas law equation \(PV = nRT\). Since \(T\) and \(P\) are constants, we can simplify this formula to show \(V = n\cdot (RT/P)\). Thus, \(V\) is directly proportional to \(n\).

Provide Final Explanation

Since all other variables are constant in the simplified equation, a change in \(n\) would directly result in a proportionate change in \(V\).