If balloon is descending in vacuum, a = g. Otherwise,
Let V be the volume of balloon. Let ρ be the density of balloon. ρ = m/V
Let d be the density of air in the atmosphere at the location where balloon is descending.
There is a force of buoyancy upwards on balloon exerted by air in the atmosphere.
Net Force on balloon downwards = m g - d V g = (m - d V) g
Acceleration downwards of the balloon = (m - d V) g / m = [1 - d V/m] g
a = [ 1 - d/ρ ] g
If we want to be more precise, there is also a drag (damping) or contact force of air resistance on the balloon = b v, where v is the instant velocity of balloon.
a = g - (d/ρ) g - b v, where v =
This is a second order differential equation. It is to be solved to get an exponentially decreasing function of time.