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 molar mass of the mixture is

Options

A. `6g`
B. `(13)/(7)g`
C. `(18)/(7)g`
D. None

Explanation

To find the equivalent molar mass of the mixture of helium and hydrogen, we can follow these steps:

### Step 1: Identify the number of moles and molar masses
- Number of moles of helium (N1) = 5 moles
- Molar mass of helium (M1) = 4 g/mol
- Number of moles of hydrogen (N2) = 2 moles
- Molar mass of hydrogen (M2) = 2 g/mol

### Step 2: Use the formula for equivalent molar mass
The equivalent molar mass (M_eq) of a mixture can be calculated using the formula:

\[ M_{eq} = \frac{N_1 \cdot M_1 + N_2 \cdot M_2}{N_1 + N_2} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:

\[ M_{eq} = \frac{(5 \cdot 4) + (2 \cdot 2)}{5 + 2} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:

\[ 5 \cdot 4 = 20 \]
\[ 2 \cdot 2 = 4 \]
\[ \text{Numerator} = 20 + 4 = 24 \]

Calculating the denominator:

\[ 5 + 2 = 7 \]

### Step 5: Calculate the equivalent molar mass
Now, substituting back into the equation:

\[ M_{eq} = \frac{24}{7} \]

### Step 6: Final result
Thus, the equivalent molar mass of the mixture is:

\[ M_{eq} \approx 3.43 \, \text{g/mol} \]

### Summary
The equivalent molar mass of the mixture of helium and hydrogen is approximately \( \frac{24}{7} \) g/mol or about 3.43 g/mol.

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