Chapter 13, Problem 1STP

Interpretation Introduction

Interpretation:

The pressures of helium between a large balloon and a small balloon have to be compared.

Concept Introduction:

The ideal gas law can be expressed as-

  $\mathrm{PV}=nRT$ Where, R is universal gas constant.

The pressure of a gas depends on the number of moles of gas and the pressure of a gas is directly proportional to the number of moles when volume (V) and temperature (T) remain constant.

  $\mathrm{P}\propto n$

The pressure of a gas depends on the volume and inversely proportional to the volume when number of moles and temperature remain constant.

  $\mathrm{P}\propto \frac{1}{V}$

Answer to Problem 1STP

D. The pressures are essentially the same and about equal to atmospheric pressure.

Explanation of Solution

The pressure of a gas depends on the number of moles of gas and directly proportional to the number of moles when volume and temperature remain constant. Again the pressure of a gas depends on the volume of gas and inversely proportional to the volume when number of moles and temperature remain constant.

We can only compare the pressure with respect to one of the variables the number of moles of gas or the volume when other remain constant. In the given question, two balloons with different size are mentioned but does not concern about the number of moles of gas present in the balloons or the volume. So, from the given data we can say that the pressures of a large balloon and a small balloon are essentially the same and about equal to atmospheric pressure.

Conclusion

Reasons for incorrect options:

The pressures of a large balloon and a small balloon are essentially the same and about equal to atmospheric pressure.

So the answer is option D.

That means other options that is,

A. The pressure in the large balloon is greater than the pressure in the small balloon. This is best explained by the fact that there are more moles of gas in the large balloon, thus greater

pressure.

B. The pressure in the small balloon is greater than the pressure in the large balloon. This is best explained by the fact that as the volume of a container decreases, the pressure of the gas increases.

C. The pressure in the large balloon is greater than the pressure in the small balloon. The fact that there is greater pressure in the balloon is why the volume is larger; as the particles push more on the inside, the volume increases.

are found to be incorrect.