Question

A cylinder containing 14.50 L of helium gas at a pressure of 170.0 atm is to be used to fill toy balloons to a pressure of 1.000 atm. Each inflated balloon has a volume of 2.500 L. What is the maximum number of balloons that can be inflated? Report your answer to 1 decimal place. (Remember that 14.50 L of helium at 1.000 atm will remain in the exhausted (empty) cylinder)

Answer 1

we need to determine the volume of the gas in the cylinder when the pressure is decreased to 1.0atm

write down the known and unknown quantities

P₁ = 170.0 atm

V₁ = 14.50 L

P₂ = 1.0 atm

V₂ = ?

Use Boyle's law to find the unknown volume

P₁V₁ = P₂V₂

V₂ = $\frac{P_1V_1}{P_2}$

V₂ = $\frac{170.0atm×14.50L}{1.0atm}$

V₂ = 170×14.50 L

V₂ = 2465 L

Calculate the number of ballons that can be filled up by dividing the total volume of gas at 1.0 atm by the volume of a single ballon

N_balloon = $\frac{V_2}{V_balloon}$

N_balloon = $\frac{2465}{2.5}$

N_balloon = 986 ballons

N_ballons = 0.9×10³ balloons