  In this paper, we study the asymptotic behavior of the traces of Hecke
operators for spherical discrete automorphic representations of fixed level on
general split reductive groups over $\mathbb{Q}$. Under a condition on the
analytic behavior of intertwining operators, which is known for the classical
groups and the exceptional group $G_2$, we obtain the expected asymptotics in
terms of the spherical Plancherel measure and an explicit estimate for the
remainder.
