  We consider the parabolic Anderson model (PAM) $\partial_t u = \frac12 \Delta
u + \xi u$ in $\mathbb R^2$ with a Gaussian (space) white-noise potential
$\xi$. We prove that the almost-sure large-time asymptotic behaviour of the
total mass at time $t$, written $U(t)$, is given by $\log U(t)\sim \chi t \log
t$ for $t \to \infty$, with the deterministic constant $\chi$ identified in
terms of a variational formula. In earlier work of one of the authors this
constant was used to describe the asymptotic behaviour $\boldsymbol
\lambda_1(Q_t)\sim\chi\log t$ of the principal eigenvalue
$\boldsymbol\lambda_1(Q_t)$ of the Anderson operator with Dirichlet boundary
conditions on the box $Q_t= [-\frac{t}{2},\frac{t}{2}]^2$.
