Ch.10 - Gases

Problem 105

Chapter 10, Problem 105

Consider the arrangement of bulbs shown in the drawing. Each of the bulbs contains a gas at the pressure shown. What is the pressure of the system when all the stopcocks are opened, assuming that the temperature remains constant? (We can neglect the volume of the capillary tubing connecting the bulbs.)

Verified step by step guidance

Step 1: Identify the initial pressures and volumes of the gases in each bulb: O2 (600 mmHg, 1.0 L), Ne (430 mmHg, 0.5 L), and He (500 mmHg, 2.0 L).

Step 2: Use the ideal gas law to determine the number of moles of each gas. The ideal gas law is given by PV = nRT. Since the temperature and R are constant, we can use the relationship n = PV/RT.

Step 3: Calculate the total number of moles of gas in the system by summing the moles of O2, Ne, and He.

Step 4: Determine the total volume of the system by summing the volumes of the individual bulbs: V_total = V_O2 + V_Ne + V_He.

Step 5: Use the ideal gas law again to find the final pressure of the system when all stopcocks are opened. The final pressure P_final can be found using P_final = (n_total * RT) / V_total.

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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 a gas through the equation PV = nRT. In this scenario, since the temperature is constant and the gases are mixed, the law helps predict how the pressures will change when the stopcocks are opened, allowing for the calculation of the final pressure in the system.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle is crucial for solving the problem, as it allows us to calculate the total pressure by adding the pressures of the individual gases present in the bulbs once the stopcocks are opened.

Volume and Pressure Relationship

The relationship between volume and pressure is described by Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. In this case, the different volumes of the gas bulbs will affect the final pressure when they are combined, necessitating consideration of both the pressures and volumes of the gases involved.

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