Question

A cylinder containing 44.0 L of helium gas at a pressure of 170 atm is to be used to fill toy balloons to a pressure of 1.1 atm. Each inflated balloon has a volume of 2.0 L. What is the maximum number of balloons that can be inflated? (Remember that 44.0 L of helium at 1.1 atm pressure will remain in the 'exhausted' cylinder) Round your answer to two significant digits.

Answer 1

Answer:- 3400 balloons

Solution:- Originally the helium gas is at 170 atm pressure and there are 44.0 L of it. The pressure of the balloon filled by this has is 1.1 atm and the volume is 2.0 L. Let's first calculate the pressure of helium gas at 1.1 atm of pressure using Boyle's law, "At constant temperature, the volume of the gas is inversely proportional to the pressure."

The equation used for this is:

$P_1V_1=P_2V_2$

$P_1$ = 170 atm

$P_2$ = 1.1 atm

$V_1$ = 44.0 L

$V_2$ = ?

Let's plug in the values and solve this for $V_2$ .

$170atm(44.0L)=1.1atm(V_2)$

$V_2=\frac{170atm(44.0L)}{1.1atm}$

$V_2$ = 6800 L

Now, 44.0 L of the gas is remaining in the exhausted cylinder at 1.1 atm of pressure.

So, the volume of the gas used to fill the balloons = 6800 L - 44.0 L= 6756 L

2.0 L is the volume of one balloon filled by the helium gas. 6756 L would be the volume of how many balloons?

We could easily solve this on dividing the above calculated total volume used to fill the balloons by the volume of one balloon.

$6756L(\frac{1balloon}{2.0L})$

= 3378 balloons

The answer is asked to be reported with two sig figs, so it could be written as 3400 balloons.

Hence, 3400 balloons could be filled by the helium gas.