A balloon filled with oxygen is placed in a tank full of hydrogen gas at the same pressure is pricked with a sharp pointed needle. The volume of balloon just after the pricking would be

Options

A. Shrunk
B. Enlarge
C. Completely collapsed
D. remains unchanged in size

Answer

To solve the problem, we need to analyze the behavior of gases when a balloon filled with oxygen is pricked in a tank of hydrogen gas. Here’s the step-by-step solution:

### Step 1: Understand the Initial Conditions
- A balloon is filled with oxygen gas (O₂) and is placed in a tank filled with hydrogen gas (H₂).
- Both the balloon and the tank are at the same pressure.

**Hint:** Consider the properties of gases and the conditions of pressure and concentration.

### Step 2: Analyze the Effect of Pricking the Balloon
- When the balloon is pricked with a sharp needle, a small hole is created.
- The oxygen gas inside the balloon will start to escape through the hole due to the pressure difference and concentration gradient.

**Hint:** Think about the movement of gas molecules and how they behave when there is an opening.

### Step 3: Consider the Diffusion of Gases
- According to Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
- The molar mass of oxygen (O₂) is approximately 32 g/mol (16 g/mol for each oxygen atom), while the molar mass of hydrogen (H₂) is approximately 2 g/mol.

**Hint:** Remember that lighter gases diffuse faster than heavier gases.

### Step 4: Calculate the Rate of Diffusion
- Using Graham's law, we can set up the ratio of the rates of diffusion:
\[ \frac{R_{H2}}{R_{O2}} = \sqrt{\frac{M_{O2}}{M_{H2}}} \]
Substituting the values:
\[ \frac{R_{H2}}{R_{O2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \]
- This means that hydrogen diffuses into the balloon at a rate 4 times faster than oxygen diffuses out.

**Hint:** Focus on how the rates of diffusion relate to the behavior of the gases in the balloon.

### Step 5: Determine the Change in Volume of the Balloon
- Since hydrogen is entering the balloon at a faster rate than oxygen is leaving, the overall effect will be that the volume of the balloon increases.
- Therefore, just after the pricking, the balloon will enlarge due to the influx of hydrogen gas.

**Hint:** Consider the net movement of gas molecules and how it affects the volume of the balloon.

### Conclusion
- The volume of the balloon just after pricking would be **enlarged**.

### Final Answer
The volume of the balloon just after pricking would be enlarged.

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