Question

A tank with a volume of 0.15 m3 contains 27?C helium gas at a pressure of 100 ATM. How many balloons can be blown up if each filled balloon is a sphere 30 cm in diameter at 27?C and absolute pressure of 1.2 ATM?

884 balloons

598 balloons

776 balloons

963 balloons

442 balloons

Answer 1

Ans:-

Given data V= 0.15m^3*1000L/m^3= 150L

T = 27deg= 300k P= 100ATM
R =0 .082 mol*K/L*atm

First solve for the number of moles in the tank:
PV = nRT
100 * 150L = n * 0.082 mol*K/L*atm * 300
n = 609.79 mol

Now:
P = 1.2 atm r= 0.15m
V = 4/3pir^3 = 4/3 pi (0.15m)^3 = 0.01413m^3 = 14.13L
R = 0.082 mol*K/L*atm
T =300k

solve for the number of moles per balloon
PV = nRT
1.2 atm * 14.13L = n * 0.082 mol*K/L*atm * 300
n = 0.6893 mol

balloons = n_tank/n_balloons
n_tank/n_balloons = 609.79 mol / 0.6893 mol = 884.69balloons