At present, automobile batteries are sealed. When lead storage batteries discharge, they produce hydrogen. Suppose the void volume in the battery is 100 mL at 1 atm of pressure and 25 degrees Celsius. What would be the pressure increase if 0.05 g of Hydrogen were produced by the discharge of the battery? Does this present a problem? Do you know why sealed lead storage batteries were not used in the past?

You can use
PV = nRT
P = nRT / V
now you have n(number of moles of H2 ) , R = 0.0821 atm L /K .mol  and temp ( 25 + 273 )K ,
V is the volume = 100mL = 0.1L
new pressure = 1 atm + pressure due to H2
yes it can cause a problem because H2 is highly combustible gas and its formation in a sealed battery could lead to explosion.