A mixture of `4 g` of hydrogen and `8 g` of helium at (NTP) has a dencity about.

Options

A. `0.22 kg//m^3`
B. `0.62 kg//m^3`
C. `1.12 kg//m^3`
D. `0.13 kg//m^3`

Explanation

To find the density of a mixture of 4 g of hydrogen and 8 g of helium at Normal Temperature and Pressure (NTP), we can follow these steps:

### Step 1: Calculate the number of moles of hydrogen (H₂)
The molar mass of hydrogen (H₂) is approximately 2 g/mol.
\[ \text{Number of moles of H₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{4 \, \text{g}}{2 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 2: Calculate the number of moles of helium (He)
The molar mass of helium (He) is approximately 4 g/mol.
\[ \text{Number of moles of He} = \frac{\text{mass}}{\text{molar mass}} = \frac{8 \, \text{g}}{4 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 3: Calculate the total number of moles in the mixture
\[ \text{Total number of moles} = \text{moles of H₂} + \text{moles of He} = 2 + 2 = 4 \, \text{moles} \]

### Step 4: Calculate the total volume of the gas at NTP
At NTP, 1 mole of an ideal gas occupies 22.4 liters.
\[ \text{Total volume} = \text{Total moles} \times 22.4 \, \text{L} = 4 \, \text{moles} \times 22.4 \, \text{L/mole} = 89.6 \, \text{L} \]

### Step 5: Calculate the total mass of the gas
\[ \text{Total mass} = \text{mass of H₂} + \text{mass of He} = 4 \, \text{g} + 8 \, \text{g} = 12 \, \text{g} \]

### Step 6: Convert the total mass to kilograms
\[ \text{Total mass in kg} = \frac{12 \, \text{g}}{1000} = 0.012 \, \text{kg} \]

### Step 7: Convert the total volume to cubic meters
\[ \text{Total volume in m}^3 = \frac{89.6 \, \text{L}}{1000} = 0.0896 \, \text{m}^3 \]

### Step 8: Calculate the density of the gas mixture
Density (\(\rho\)) is defined as mass per unit volume.
\[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{0.012 \, \text{kg}}{0.0896 \, \text{m}^3} \approx 0.134 \, \text{kg/m}^3 \]

### Conclusion
The density of the mixture of 4 g of hydrogen and 8 g of helium at NTP is approximately **0.134 kg/m³**.

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