What is the ratio of diffusion rate of oxygen to hydrogen?

Options

A. `1:4`
B. `4:1`
C. `1:8`
D. `8:1`

Explanation

To find the ratio of the diffusion rate of oxygen (O₂) to hydrogen (H₂), we can use Graham's law of effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The formula can be expressed as:

\[ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} \]

Where:
- \( r_1 \) is the rate of diffusion of gas 1 (O₂),
- \( r_2 \) is the rate of diffusion of gas 2 (H₂),
- \( M_1 \) is the molar mass of gas 1 (O₂),
- \( M_2 \) is the molar mass of gas 2 (H₂).

### Step 1: Identify the molar masses
- Molar mass of hydrogen (H₂) = 2 g/mol (since H = 1 g/mol and there are 2 hydrogen atoms).
- Molar mass of oxygen (O₂) = 32 g/mol (since O = 16 g/mol and there are 2 oxygen atoms).

### Step 2: Apply Graham's law
Using the formula, we can substitute the molar masses:

\[ \frac{r_{O_2}}{r_{H_2}} = \sqrt{\frac{M_{H_2}}{M_{O_2}}} = \sqrt{\frac{2}{32}} \]

### Step 3: Simplify the ratio
Now, simplify the fraction inside the square root:

\[ \frac{2}{32} = \frac{1}{16} \]

So we have:

\[ \frac{r_{O_2}}{r_{H_2}} = \sqrt{\frac{1}{16}} = \frac{1}{4} \]

### Final Answer
Thus, the ratio of the diffusion rate of oxygen to hydrogen is:

\[ \frac{r_{O_2}}{r_{H_2}} = \frac{1}{4} \]