Chapter 13, Problem 58A

Interpretation Introduction

Interpretation:

The tank will have to contain helium at the pressure of 750mmHg after the balloons are filled then the number of balloons inflated with the gas in the tank is to be determined.

Concept introduction:

The ideal gases are those gases which obey the ideal gas equation and the ideal gas equation is written as

  $\text{PV}\text{= nRT}$

Where, P = pressure of the gas

V = Volume of the gas

R = Gas constant

T = temperature of the gas

Answer to Problem 58A

The volume of helium gas is used in the filling of the balloon is $\text{187}\text{.886}\text{L}$ . So, the numbers of balloons filled are $\text{125}$ .

Explanation of Solution

Given information:

Temperature = $\text{25°C}$

Initial pressure, ${\text{P}}_{\text{1}}\text{}\text{= }\text{}\text{8}\text{.40}\text{atm}$

Final pressure,

  $\begin{array}{l}{\text{P}}_{\text{2}}\text{}\text{= }\text{}\text{755}\text{mmHg}\\ \text{=}\frac{\text{755}}{\text{760}}\text{=}\text{0}\text{.9934}\text{atm}\end{array}$

Now, based on this result

The pressure is reduced from $\text{8}\text{.40atm}$ to $\text{0}\text{.993atm}$ .

Now, according to ideal gas law,

  $\begin{array}{l}{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}\text{=}{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}\\ {\text{V}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{P}}_{\text{2}}}\\ \text{=}\frac{\text{8}\text{.40×25}\text{.2}}{\text{0}\text{.993}}\\ \text{=}\text{213}\text{.086}\text{L}\end{array}$

The gas has expanded to the volume $\text{213}\text{.086}\text{L}$ , when the pressure inside the tank is 755mmHg.

According to the calculation, the pressure is reduced to $\text{0}\text{.993atm}$ , so no more helium gas is produced. Thus, 25.2L helium gas will be left in the tank.

So, the volume of helium gas which is used in filling the balloons is 187.886L.

  $\left(\because \text{213}\text{.086-}\text{25}\text{.2}\right)$

Hence, the numbers of filled balloons are calculated as:

  $\text{n}\text{=}\frac{\text{187}\text{.886}}{\text{1}\text{.5}}\text{=}\text{125}\text{.2}\text{=}\text{125}\left(\text{approximate}\text{value}\right)$

Conclusion

On the basis of the remaining volume of the helium in the tank, the filled balloons are $\text{125}$ .