Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium `M_(1) = 4g` and that of hydrogen `M_(2) = 2g`
The equivalent degree of freedom f of the mixture is

Options

A. `3.57`
B. `1.14`
C. `4.4`
D. None

Explanation

To find the equivalent degree of freedom \( f \) of the mixture of helium and hydrogen, we can follow these steps:

### Step 1: Determine the degrees of freedom for each gas
- For a monoatomic gas like helium, the degrees of freedom \( f_1 \) is given by:
\[ f_1 = 3 \]
- For a diatomic gas like hydrogen, the degrees of freedom \( f_2 \) is given by:
\[ f_2 = 5 \]

### Step 2: Calculate the total degrees of freedom for the mixture
- The total degrees of freedom for the mixture can be calculated using the formula:
\[ f_{\text{mix}} = \frac{n_1 f_1 + n_2 f_2}{n_1 + n_2} \]
where \( n_1 \) and \( n_2 \) are the number of moles of helium and hydrogen respectively.

### Step 3: Substitute the values
- Given:
- \( n_1 = 5 \) moles of helium
- \( n_2 = 2 \) moles of hydrogen
- Substitute the values into the formula:
\[ f_{\text{mix}} = \frac{5 \cdot 3 + 2 \cdot 5}{5 + 2} \]

### Step 4: Calculate the numerator and denominator
- Calculate the numerator:
\[ 5 \cdot 3 + 2 \cdot 5 = 15 + 10 = 25 \]
- Calculate the denominator:
\[ 5 + 2 = 7 \]

### Step 5: Compute the equivalent degree of freedom
- Now, substitute the values into the equation:
\[ f_{\text{mix}} = \frac{25}{7} \approx 3.57 \]

### Conclusion
- The equivalent degree of freedom \( f \) of the mixture is approximately \( 3.57 \).