Question

Consider two bulbs separated by a valve. Both bulbs are maintained at the same temperature. Assume that when the valve between the two bulbs is closed, the gases are sealed in their respective bulbs. When the valve is closed, the following data apply: Bulb A Bulb B Gas Ne CO V 2.50 L 2.00 L P 1.09 atm 0.773 atm Assuming no temperature change, determine the final pressure inside the system after the valve connecting the two bulbs is opened. Ignore the volume of the tube connecting the two bulbs.

Short answer

" Answer: To determine the final pressure of the system, we need to follow these steps: 1) Calculate the initial moles of gas in each bulb using the Ideal Gas Law; 2) Calculate the total number of moles in the system by adding the moles of gas in both bulbs; 3) Calculate the total volume of the system by adding the volumes of each bulb; 4) Calculate the final pressure using the Ideal Gas Law, with the total moles and total volume. After completing these steps and solving for the final pressure (P_final), we can find the final pressure inside the system after the valve connecting the two bulbs is opened.

Step-by-step solution

Calculate the initial moles of gas in each bulb

Apply the Ideal Gas Law (PV=nRT) for each bulb to calculate the initial moles of gas in each bulb. In this equation, P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L*atm/mol*K), and T is the temperature. Bulb A: P_A = 1.09 atm V_A = 2.50 L R = 0.0821 L*atm/mol*K (ideal gas constant) T (temperature) is equal in both bulbs. So, n_A = (P_A * V_A) / (R * T) Bulb B: P_B = 0.773 atm V_B = 2.00 L So, n_B = (P_B * V_B) / (R * T)

Calculate the total number of moles in the system

Now, calculate the total number of moles of gas in the system by adding the moles of gas in both bulbs A and B. n_total = n_A + n_B

Calculate the total volume of the system

Find the total volume of the system by adding the volumes of each bulb: V_total = V_A + V_B

Calculate the final pressure of the system

Now that we have the total moles of gas and the total volume of the system, we can calculate the final pressure using the Ideal Gas Law. Since the temperature is constant, we can use the same equation to find the final pressure: Final Pressure, P_final = (n_total * R * T) / V_total Using the values calculated in steps 1-3, plug in the values and solve for P_final: P_final = ((n_A + n_B) * R * T) / (V_A + V_B) Once you solve for P_final, you will find the final pressure inside the system after the valve connecting the two bulbs is opened.