The apparatus shown consists of three bulbs connected by stopcocks. What is the pressure inside the system when the stopcocks are opened? Assume that the lines connecting the bulbs have zero volume and that the temperature remains constant. (LO 10.3, 10.7)(a) 1.10 atm (b) 1.73 atm(c) 4.14 atm (d) 1.41 atm

Verified step by step guidance

1. Step 1: Identify the initial pressures and volumes of each bulb. Let P_A, P_B, and P_C be the pressures in bulbs A, B, and C respectively, and V_A, V_B, and V_C be the volumes of bulbs A, B, and C respectively.
2. Step 2: Use the ideal gas law (PV = nRT) to express the number of moles of gas in each bulb. Since the temperature (T) and the gas constant (R) are constant, the number of moles (n) in each bulb can be written as n_A = P_A * V_A / RT, n_B = P_B * V_B / RT, and n_C = P_C * V_C / RT.
3. Step 3: When the stopcocks are opened, the gases will mix and the total volume will be the sum of the individual volumes (V_total = V_A + V_B + V_C). The total number of moles of gas will be the sum of the moles in each bulb (n_total = n_A + n_B + n_C).
4. Step 4: Use the ideal gas law again to find the final pressure (P_final) in the system. The total number of moles (n_total) and the total volume (V_total) are known, so P_final = (n_total * RT) / V_total.
5. Step 5: Substitute the expressions for n_A, n_B, and n_C into the equation for n_total, and then solve for P_final. This will give you the final pressure inside the system when the stopcocks are opened.

Key Concepts

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 volume of the connecting lines is negligible, the pressure in the system can be analyzed using this law to determine how the pressures in the individual bulbs affect the overall pressure when the stopcocks are opened.

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. When the stopcocks are opened, the gases from the three bulbs will mix, and the total pressure can be calculated by adding the partial pressures of the gases in bulbs A, B, and C, assuming they behave ideally.

Constant Temperature Process

A constant temperature process, or isothermal process, occurs when a gas expands or compresses without changing its temperature. In this question, since the temperature remains constant, the relationship between pressure and volume for the gases in the bulbs will follow the principles of isothermal behavior, allowing for the application of the Ideal Gas Law and Dalton's Law to find the final pressure in the system.