= Solution
Let $G$ be the remaining gas <mass>, $S$ the formed stellar <mass>, and $G_0$ the initial gas <mass>; initially $S=0$ and the <gas-phase metallicity> is zero. Take the <stellar yield> $y$ and the <mass-loading factor> $\nu$ to be constant, with homogeneous mixing and no <galactic gas inflow>. With the specified zero bulk return, <mass conservation> gives
$$
dG=-(1+\nu)\,dS,\qquad G=G_0-(1+\nu)S.
$$
New metals add $y\,dS$, while <star formation> and the <galactic outflow> remove metals at the existing <gas-phase metallicity> $Z$. Thus
$$
d(GZ)=y\,dS-Z(1+\nu)\,dS,
\qquad G\,dZ=y\,dS=-\frac{y}{1+\nu}\,dG.
$$
The <leaky-box model of galactic chemical evolution> therefore gives
$$
Z=\frac{y}{1+\nu}\ln\frac{G_0}{G}.
$$
For the usual <gas fraction of a galaxy>, $\mu=G/(G+S)$, the denominator is the baryonic <mass> still in the system, which decreases under the <galactic outflow>. Since $G_0=G+(1+\nu)S$, we have $G_0/G=1+(1+\nu)(1-\mu)/\mu$. \b[In the remaining-mass convention,]
$$
\boxed{Z(\mu)=\frac{y}{1+\nu}\ln\left[\frac{1+\nu(1-\mu)}{\mu}\right].}
$$
If instead $\mu$ denotes $G/G_0$ relative to the fixed initial reservoir, the same calculation gives $\boxed{Z=y\ln(1/\mu)/(1+\nu)}$. Stating the denominator matters: these two <gas fraction of a galaxy> conventions coincide for the <closed-box model of galactic chemical evolution>, recovered at $\nu=0$, but differ when gas escapes. Neglecting bulk return while retaining a nonzero <stellar yield> is the intended trace-metal approximation.
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