Chapter 13, Problem 74A

Interpretation Introduction

Interpretation:

If the balloon will pop or not is to be identified under the given information.

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 74A

Yes, the balloon will be popped because its volume under the given temperature and pressure is $\text{0}\text{.896}\text{L}$ which is less than its maximum volume.

Explanation of Solution

Given information:

The maximum volume of the balloon = $\text{3L}$

Volume of $\text{HCl}$ = $\text{100}\text{.0}\text{ml}$

Concentration of $\text{HCl}$ = $\text{2}\text{.00M}$

Pressure = $\text{1}\text{atm}$

Temperature = $\text{25°C}\text{=}\text{25+273}\text{=}\text{298K}$

Calculation:

The reaction is as follows:

  $\text{Zn}\left(\text{s}\right)\text{+}2\text{HCl}\left(\text{aq}\right)\to {\text{ZnCl}}_{\text{2}}\left(\text{aq}\right)\text{+}{\text{H}}_{\text{2}}\left(\text{g}\right)$

  $\begin{array}{l}\text{number}\text{of}\text{moles}\text{of}\text{Zn}\text{=}\frac{\text{volume}\text{given}\text{in}\text{litre}}{\text{22}\text{.4L}}\\ {\text{n}}_{\text{Zn}}\text{=}\frac{\text{0}\text{.1L}}{\text{22}\text{.4L}}\\ \text{=}\text{0}\text{.044}\text{moles}\\ \text{if}\text{1}\text{mole}\text{of}\text{Zn}\text{=}\text{1}\text{mole}\text{of}{\text{H}}_{\text{2}}\\ \text{0}\text{.04}\text{moles}\text{of}\text{Zn}\text{=}\text{0}\text{.04}\text{moles}\text{of}{\text{H}}_{\text{2}}\\ \text{Then,}\text{find}\text{the}\text{volume}\text{of}{\text{H}}_{\text{2}}\end{array}$

  $\begin{array}{l}{\text{n}}_{{\text{H}}_{\text{2}}}\text{=}\frac{\text{volume}\text{in}\text{L}}{\text{22}\text{.4L}}\\ \text{0}\text{.04}\text{=}\frac{\text{volume}}{\text{22}\text{.4}}\\ \text{volume}\text{=}\text{0}\text{.04×22}\text{.4}\\ \text{=}\text{0}\text{.896}\text{L}\end{array}$

Conclusion

On the bases of the given information, the volume of the balloon is $\text{0}\text{.896}\text{L}$ which less than the maximum capacity of the balloon. So, the balloon will pop up.