CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 9, Exercise 1 Solution
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Finding Volume from the Ideal Gas Law

PROBLEM
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2 mol of an ideal gas is held at a constant pressure of 1 atm and a
temperature of 350 K. Using PV = nRT (with R = 0.0821 L.atm/(mol.K)),
calculate the gas's volume.

SOLUTION
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Starting from the ideal gas law:

    PV = nRT

Rearranged to solve for volume:

    V = nRT / P

Substitute the given values:

    n = 2 mol
    R = 0.0821 L.atm/(mol.K)
    T = 350 K
    P = 1 atm

    V = (2 x 0.0821 x 350) / 1
    V = 57.47 / 1
    V = 57.47 L

ANSWER: The gas occupies approximately 57.47 L.

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WHY THIS WORKS AS AN ANSWER

Rearranging PV = nRT into V = nRT/P isolates the one unknown quantity
(volume) on its own, using the three given quantities (amount,
temperature, pressure) directly. This equation combines all four
empirical gas laws from the chapter's own reference table at once:
increasing n or T increases volume (consistent with Avogadro's and
Charles's Laws respectively), while increasing P would decrease
volume (consistent with Boyle's Law) - all captured correctly within
this single combined equation, exactly as Clapeyron and Mendeleev's
real 1834 unification intended.