The apparatus given below is used to study the diffusion of a number of gases at the same temperature and pressure.

Which of the following pairs of gases would diffuse into vacuum at the same speed ? (Given atomic mass of H = 1 u, C = 12 u, N = 14 u, O = 16 u)

Question

The apparatus given below is used to study the diffusion of a number of gases at the same temperature and pressure.

Which of the following pairs of gases would diffuse into vacuum at the same speed ? (Given atomic mass of H = 1 u, C = 12 u, N = 14 u, O = 16 u)

Accepted Answer

To determine which pair of gases would diffuse into a vacuum at the same speed, we need to consider Graham's law of effusion. According to Graham's law, the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. Therefore, for two gases to diffuse at the same speed, they must have the same molar mass.

Let's analyze each option:

1. **Option 1: NH$_5$ and H$_2$**

- NH$_5$ is not a chemically stable or recognized compound, so we cannot calculate its molar mass. However, assuming a hypothetical scenario, NH$_5$ would have a molar mass of approximately 19 u (1 for H and 14 for N).
   - H$_2$ has a molar mass of 2 u.
   - These two gases have significantly different molar masses, so they would not diffuse at the same speed.

2. **Option 2: CO and SO$_2$**

- CO (carbon monoxide) has a molar mass of 28 u (12 for C and 16 for O).
   - SO$_2$ (sulfur dioxide) has a molar mass of 64 u (32 for S and 32 for two O atoms).
   - The molar masses are different, so these gases would not diffuse at the same speed.

3. **Option 3: CO and N$_2$**

- CO (carbon monoxide) has a molar mass of 28 u (12 for C and 16 for O).
   - N$_2$ (nitrogen gas) also has a molar mass of 28 u (14 for each N atom).
   - Since both gases have the same molar mass, they would diffuse into a vacuum at the same speed. This is why Option 3 is the correct answer.

4. **Option 4: NH$_3$ and N$_2$**

- NH$_3$ (ammonia) has a molar mass of 17 u (14 for N and 3 for H).
   - N$_2$ (nitrogen gas) has a molar mass of 28 u (14 for each N atom).
   - The molar masses are different, so these gases would not diffuse at the same speed.

In conclusion, Option 3 is correct because CO and N$_2$ have the same molar mass, allowing them to diffuse at the same speed according to Graham's law of effusion.