At 300 k , 500ml of helium diffuses in 30 min , what is the time in hours taken for 100 ml of SO2 to diffuse under same conditions ..

To determine the time it takes for 100 ml of sulfur dioxide (SO2) to diffuse under the same conditions as helium, we can use Graham's law of effusion. This law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. Let's break this down step by step.

Understanding Graham's Law

Graham's law can be expressed mathematically as:

Rate1 / Rate2 = √(Molar Mass2 / Molar Mass1)

Where:

• Rate1 is the rate of diffusion of the first gas (helium in this case).
• Rate2 is the rate of diffusion of the second gas (sulfur dioxide).
• Molar Mass1 is the molar mass of the first gas (helium).
• Molar Mass2 is the molar mass of the second gas (sulfur dioxide).

Step 1: Identify Molar Masses

The molar mass of helium (He) is approximately 4 g/mol, while the molar mass of sulfur dioxide (SO2) is about 64 g/mol. This significant difference in molar mass will play a crucial role in our calculations.

Step 2: Calculate the Rate of Diffusion

Since we know that helium diffuses 500 ml in 30 minutes, we can calculate its rate of diffusion:

Rate of He = 500 ml / 30 min = 16.67 ml/min

Step 3: Apply Graham's Law

Now, we can set up the equation using Graham's law:

Rate of He / Rate of SO2 = √(Molar Mass of SO2 / Molar Mass of He)

Substituting the values:

16.67 ml/min / Rate of SO2 = √(64 g/mol / 4 g/mol)

This simplifies to:

16.67 ml/min / Rate of SO2 = √(16)

16.67 ml/min / Rate of SO2 = 4

Step 4: Solve for Rate of SO2

Now, we can rearrange the equation to find the rate of diffusion for SO2:

Rate of SO2 = 16.67 ml/min / 4 = 4.167 ml/min

Step 5: Calculate Time for SO2 to Diffuse

Next, we need to find out how long it takes for 100 ml of SO2 to diffuse at this rate:

Time = Volume / Rate

Time = 100 ml / 4.167 ml/min ≈ 24 minutes

Step 6: Convert Minutes to Hours

Finally, to convert minutes into hours:

24 minutes / 60 minutes/hour = 0.4 hours

In summary, under the same conditions, it would take approximately 0.4 hours for 100 ml of sulfur dioxide to diffuse. This example illustrates how the principles of gas diffusion can be applied to different gases based on their molar masses.