  We investigate the errors due to the use of unphysical values of light quark
masses in lattice extractions of $\alpha_s$. A functional form for the pion
mass dependence of the quarkonium mass splittings ($\Delta m$) is given as an
expansion in $m_\pi/(4\pi f_\pi)$ and $m_\pi r_B$, where $r_B$ is the
quarkonium Bohr radius. We find that, to lowest order,$\Delta m\simeq A+B
m_\pi^2$, where the scale of $B$ is given by $f_\pi^2 r_B^3$. To order
$m_\pi^4$ there are four unknown coefficients, however, utilizing multipole and
operator product expansions, symmetry arguments eliminate one of the four
unknowns. Using the central values for the lattice spacings which were
extracted using two different, unphysical values for the pion mass, we find
that the errors introduced by extrapolating to the physical regime are
comparable to the errors quoted due to other sources. Extrapolation to physical
values of the pion mass {\it increases} the value of $\alpha_s(M_Z)$, bringing
its value closer to the high energy extractions.
