= Solution
For identical, non-interacting molecules, the translational <canonical partition function> is $Q_N=q_{\rm trans}^N/N!$. <Stirling's approximation> gives the <Helmholtz free energy>
$$
A=-NkT\left[\log(q_{\rm trans}/N)+1\right].
$$
At fixed $V$, $q_{\rm trans}\propto T^{3/2}$, so differentiation gives $S=Nk[\log(q_{\rm trans}/N)+5/2]$. For one mole at the standard-state molar <volume>,
$$
\boxed{S_{m,\rm trans}^{\circ}=R\left[\log\left(\frac{q_{m,\rm trans}^{\circ}}{N_A}\right)+\frac52\right]}.
$$
Here the quoted molar translational quantity is per mole, and its ratio to $N_A$ is dimensionless. The derivative defining <entropy> is taken at fixed <volume> before inserting the standard-state <volume>; differentiating along a constant-pressure path would give the wrong additive constant.
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