a spherical glass bulb of radius 100cm contain a concentric rubber balloon that contains N2 gas and remaining space contain 50 g H2. in the given condition radius of rubber balloon was 40 cm.Now the seal is broken and 26 g H2 was further added and sealed.What is the radius of rubber balloon now?
Answers
Answer:
Explanation:
Given A spherical glass bulb of radius 100cm contain a concentric rubber balloon that contains N2 gas and remaining space contain 50 g H2. in the given condition radius of rubber balloon was 40 cm.Now the seal is broken and 26 g H2 was further added and sealed.What is the radius of rubber balloon now?
Radius of spherical bulb = 0.1 m
Radius of balloon = 0.4 m
Temperature is constant.
Volume of spherical glass bulb = 4/3 π R^3
= 4/3 π (0.1)^3
Volume of balloon = 4/3 π (0.4)^3
Due to gas filled in spherical bulb, pressure on balloon is external.
Pi = initial pressure before addition of gas
Pf = final pressure after addition of gas
We know that
PV = nRT
PV = m/M RT
Pi = 50 / 2v RT
Pf = 76 / 2v RT
So Pi / Pf = 25/38
Now volume of area = volume of spherical glass bulb – volume of balloon
= 4/3 π (0.1)^3 – 4/3 π (0.4)^3
Final volume will be 4/3 π (0.1)^3 – 4/3 π (x/100)^3
We know that
PiV = nRT
PfV = nRT
Pi / Pf = 25 / 38 x 4/3 π (0.1)^3 – 4/3 π (0.4)^3 / 4/3 π (0.1)^3 – 4/3 π (x/100)^3
0.025 + 2.394 = 0.0000025 x^3
So x = 98.908