#V_1->"volume of hydrogen in cylinder"=2.82L#
#T_1->"Temperature of hydrogen in cylinder"#
#=27^@C=27+273=300K#
#P_1->"Pressure of hydrogen in cylinder"=20atm#
At NTP
#P_2->"Pressure"=1atm#
#T_2->"Temperarture"=273K#
#V_2->"Volume"=?#
By gas law
#(P_2V_2)/T_2=(P_1V_1)/T_1#
#=>V_2=(P_1V_1T_2)/(P_2T_1)#
#=(20xx2.82xx273)/(1xx300)=51.324L#
Excluding the minlmum remaining 2.82L gas in the cylinder at NTP maximum #(51.324-2.82)L=48.504L# gas can be used for filling baloons.
Volume of each spherical baloon of diameter #7cm# is
#=4/3pi(7/2)^3cm^3=4/3*22/7*7^3/8cm^3#
#=0.1796L#
Hence the maximum number of baloons that can be filled with hydrogen from the cylinder is
#="Total volume of gas"/"volume of a baloon"#
#=48.504/0.1796~~270" "#(rounding to nearest whole number)
