Out of the three states of matter, only the gases have most of the physical properties common. They neither have definite shapes nor volumes. Upon mixing they form homogeneous mixture irrespective of their nature and can also be compressed on applying pressure. In addition to these, the gases obey different gas laws such as Boyle's Law, Charles's Law, Dalton's Law of partial pressures, Graham's Law of diffusion etc. Based upon these laws, ideal gas equation `PV = nRT` has been derived.
Same mass of `CH_(4)` and `H_(2)` at taken in a container. The partial pressure caused by `H_(2)` is

Options

A. `8/9`
B. `1/9`
C. `1/2`
D. `1`

Explanation

To find the partial pressure of hydrogen gas (H₂) when the same mass of methane (CH₄) and hydrogen (H₂) are taken in a container, follow these steps:

### Step 1: Determine the mass of each gas
Assume we take 16 grams of CH₄. Since the problem states that the same mass is taken for both gases, we also have 16 grams of H₂.

### Step 2: Calculate the number of moles of each gas
- For hydrogen (H₂):
\[ \text{Molar mass of H₂} = 2 \, \text{g/mol} \]
\[ \text{Number of moles of H₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{16 \, \text{g}}{2 \, \text{g/mol}} = 8 \, \text{moles} \]

- For methane (CH₄):
\[ \text{Molar mass of CH₄} = 16 \, \text{g/mol} \]
\[ \text{Number of moles of CH₄} = \frac{16 \, \text{g}}{16 \, \text{g/mol}} = 1 \, \text{mole} \]

### Step 3: Calculate the total number of moles
\[ \text{Total moles} = \text{moles of H₂} + \text{moles of CH₄} = 8 + 1 = 9 \, \text{moles} \]

### Step 4: Calculate the mole fraction of hydrogen (H₂)
\[ \text{Mole fraction of H₂} (x_{H₂}) = \frac{\text{moles of H₂}}{\text{total moles}} = \frac{8}{9} \]

### Step 5: Determine the total pressure in the container
Assuming the total pressure (Pₜ) in the container is 1 atm (standard atmospheric pressure).

### Step 6: Calculate the partial pressure of hydrogen (H₂)
Using Dalton's Law of Partial Pressures:
\[ \text{Partial pressure of H₂} (P_{H₂}) = x_{H₂} \times Pₜ = \frac{8}{9} \times 1 \, \text{atm} = \frac{8}{9} \, \text{atm} \]

### Final Answer
The partial pressure caused by H₂ is \(\frac{8}{9} \, \text{atm}\).

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