To do this problem we need to make some assumptions and remember some basic chemistry. There is no specific values given for the pressure or temperature, but we can assume that atmospheric pressure could be the pressure at sea level (on a calm day) with a value of 1.00 atm. Room temperature could be about 27C = 300K. We will further assume that the balloon is filled with 74% nitrogen gas and 25% oxygen gas.
We can now look at the Ideal Gas Law:
PV = nRT where P is pressure, V is volume, n is number of moles, R is the ideal gas constant (0.0821 LAtm/molK), and T is temperature.
According Dalton's Law of Partial Pressure if the total pressure is 1.00 Atm, then 0.74 atm is from nitrogen and 25 atm is from oxygen.
To get the charge of electrons, we must know the number of atoms of each element. To do that we need to know the number of moles of each gas present. We thus need to solve the Ideal Gas law for n, and then calculate n for each gas. n = PV/RT
n = 0.74x3.8x10^3L/(0.0821x300) = 114 moles
n = 0.25x3.8x10^3L/(0.0821x300) = 38.6 moles.
114 moles of nitrogen gas has 1.37x10^26 atoms.
38.6 moles of oxygen gas has 4.6x10^25 atoms
Each atom of nitrogen has 7 electrons or 9.6x10^26 electrons
each atom of oxygen has 8 electrons or 3.7x10^26 electrons
So the sample of gas has 1.33x10^27 electrons. Each electron has a charge of -1.6x10^-19 Coulombs
Therefore the sample has a negative charge of -2.2 x10^8 Coulombs.
Of course this charge is neutralized by the equal, but opposite charges from the protons.