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 of what happens to the volume of the balloon filled with oxygen when it is pricked in a tank full of hydrogen gas, we can analyze the situation step by step.

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

**Hint:** Consider the properties of gases and how they behave under different conditions, particularly in terms of pressure and diffusion.

### Step 2: Identify the Effect of Pricking the Balloon
When the balloon is pricked with a sharp needle, it creates a small hole. This allows the gases inside and outside the balloon to interact.

**Hint:** Think about what happens when a container of gas is breached. Gases will move from areas of higher concentration to areas of lower concentration.

### Step 3: Analyze 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 O2 is 32 g/mol, and that of H2 is 2 g/mol.

**Hint:** Use Graham's law to compare the rates of diffusion of hydrogen and oxygen. The formula is:
\[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Molar mass}}} \]

### Step 4: Calculate the Rate of Diffusion
Using Graham's law:
\[ \frac{\text{Rate of } H2}{\text{Rate of } O2} = \sqrt{\frac{\text{Molar mass of } O2}{\text{Molar mass of } H2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \]
This means that hydrogen diffuses into the balloon at a rate 4 times that of oxygen diffusing out.

**Hint:** Remember that the higher the rate of diffusion, the faster the gas will move in or out of a given area.

### Step 5: Determine the Volume Change in the Balloon
As oxygen gas escapes from the balloon and hydrogen gas enters, the volume of the balloon will increase because hydrogen is entering at a faster rate than oxygen is leaving.

**Hint:** Consider how the balloon's elasticity allows it to expand when more gas enters compared to the amount of gas escaping.

### Conclusion
Thus, after the balloon is pricked, the volume of the balloon will increase due to the faster rate of hydrogen gas entering compared to the rate of oxygen gas escaping.

**Final Answer:** The volume of the balloon just after pricking would increase.