Ch.10 - Gases

Problem 105

Previous problem

Next problem

Chapter 10, Problem 105

An ideal gas at a pressure of 1.50 atm is contained in a bulb of unknown volume. A stopcock is used to connect this bulb with a previously evacuated bulb that has a volume of 0.800 L as shown here. When the stopcock is opened, the gas expands into the empty bulb. If the temperature is held constant during this process and the final pressure is 695 torr, what is the volume of the bulb that was originally filled with gas?

Verified step by step guidance

Convert the initial pressure from atm to torr using the conversion factor: 1 atm = 760 torr.

Apply the ideal gas law concept, which states that for a constant temperature and amount of gas, the initial and final states can be related by Boyle's Law: \( P_1V_1 = P_2V_2 \).

Identify the initial conditions: \( P_1 \) is the initial pressure in torr, and \( V_1 \) is the unknown volume of the original bulb.

Identify the final conditions: \( P_2 \) is the final pressure (695 torr), and \( V_2 \) is the total volume after expansion, which is the sum of the unknown volume and 0.800 L.

Rearrange the equation \( P_1V_1 = P_2V_2 \) to solve for \( V_1 \), the volume of the bulb that was originally filled with gas.

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. In this scenario, understanding how pressure and volume interact at constant temperature is crucial for solving the problem. The law helps predict how gas will behave when it expands or contracts.

Boyle's Law

Boyle's Law states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume (P1V1 = P2V2). This principle is essential for analyzing the gas expansion in the question, as it allows us to relate the initial and final states of the gas when the stopcock is opened.

Pressure Conversion

In this problem, pressure is given in different units (atm and torr), so understanding how to convert between these units is vital. The conversion factor is 1 atm = 760 torr. Accurately converting pressures ensures that calculations involving Boyle's Law and the Ideal Gas Law are correct and consistent.

Recommended video:

Guided course

02:20

Pressure Conversion Example

Previous problem

Next problem

Related Practice

Textbook Question

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. a. If the total pressure of the gases is 0.985 atm, calculate the partial pressure of each component of the mixture.

Textbook Question

Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (c) How many grams of glucose (C₆H₁₂O₆) would need to be metabolized to produce this quantity of CO₂? (The chemical reaction is the same as that for combustion of C₆H₁₂O₆. See Section 3.2 and Problem 10.57.)

518

views

Textbook Question

A 1.42-g sample of helium and an unknown mass of O2 are mixed in a flask at room temperature. The partial pressure of the helium is 42.5 torr, and that of the oxygen is 158 torr. What is the mass of the oxygen?

Textbook Question

You have a sample of gas at −33°C. You wish to increase the rms speed by a factor of 2. To what temperature should the gas be heated?

Textbook Question

Consider the following gases, all at STP: Ne, SF₆, N₂, CH₄. (a) Which gas is most likely to depart from the assumption of the kinetic-molecular theory that says there are no attractive or repulsive forces between molecules?

1083

views

Textbook Question

Consider the following gases, all at STP: Ne, SF₆, N₂, CH₄. (d) Which one has the highest total molecular volume relative to the space occupied by the gas?

626

views