Question

Two gas bulbs \(\mathrm{A}\) and \(\mathrm{B}\) are connected by a tube having a stopcock. Bulb A has a volume of \(100 \mathrm{~mL}\) and contains hydrogen. After opening the gas from \(A\). to the evacuated bulb \(\mathrm{B}\), the pressure falls down by \(40 \%\). The volume \((\mathrm{mL}\) ) of \(\mathrm{B}\) must be (a) 75 (b) 150 (c) 125 (d) 200

Short answer

The volume of Bulb B is 200 mL.

Step-by-step solution

Understanding the Problem

We have two connected bulbs A and B. Initially, only Bulb A contains hydrogen and Bulb B is evacuated. The volume of Bulb A is 100 mL. After the stopcock is opened, the hydrogen gas spreads into both bulbs, causing the pressure in Bulb A to fall by 40%.

Initial Conditions

The initial pressure in Bulb A can be denoted as \(P_i\). Upon opening the stopcock, the pressure drops by 40%, meaning the final pressure \(P_f\) in both bulbs is 60% of \(P_i\) since \(P_f = P_i \times 0.6\).

Key concepts

Pressure-Volume Relationship

The pressure-volume relationship is a fundamental principle of gas laws. It is often described by Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of the gas varies inversely with its volume. This means if the volume of a gas increases, its pressure decreases, and vice versa.

In our exercise, when the stopcock is opened, hydrogen gas moves from Bulb A to Bulb B. The total volume available to the gas increases. Consequently, the pressure in Bulb A decreases by 40%.

• Boyle's Law: \( P_1 \cdot V_1 = P_2 \cdot V_2 \)
• Initial volume is solely from Bulb A (100 mL).
• Final volume is the combined volume of both bulbs, leading to lower pressure.

Hydrogen Gas

Hydrogen gas, represented as \(\text{H}_2\), is a colorless and highly flammable gas. Being the lightest element, it behaves ideally under a wide range of conditions, making it a perfect candidate for experiments with gas laws.

In the exercise, hydrogen fills Bulb A initially. As it expands into Bulb B, it illustrates the gas's natural tendency to diffuse and fill the space available to it. This process reduces the pressure in Bulb A because the same amount of gas now occupies more space.

• Hydrogen is ideal for demonstrating gas behavior due to its properties.
• Diffusion illustrates hydrogen's tendency to evenly distribute in available volume.

Connected Vessels

Connected vessels allow gases to move freely between different compartments. When there is a difference in pressure, the gas naturally flows from the area of higher pressure to an area of lower pressure until equilibrium is reached.

In this scenario, two gas bulbs are linked by a tube. Initially, Bulb A is the only one containing gas, and the gas expands into Bulb B, which was evacuated at the start.

• Gas will flow until the pressure stabilizes between bulbs.
• The presence of the stopcock allows controlled experiments by controlling gas flow.
• Final pressure equilibrates across both bulbs after diffusion.

Initial and Final Conditions

By comparing initial and final conditions, we can calculate changes in pressure and volume. Initially, only Bulb A contains gas, and Bulb B is empty. The pressure in Bulb A is denoted as \(P_i\).

When the stopcock is opened, hydrogen diffuses into Bulb B, leading to a change in conditions. The pressure in Bulb A drops by 40%, indicating a new equilibrium state with pressure \(P_f = P_i \times 0.6\).

• Initial Condition: Bulb A has pressure \(P_i\), volume 100 mL.
• Final Condition: Equilibrium pressure \(P_f\) is 60% of \(P_i\).
• Combined volume determines the final pressure in both bulbs.