Two identical vessels are filled with 44g of Hydrogen and 44g of carbon dioxide at the same temperature. If the pressure of `CO_(2)` is 2 atm, the pressure of Hydrogen is

Options

A. `1 atm`
B. 44 atm
C. 2 atm
D. 22 atm

Answer

To solve the problem, we will use the ideal gas law and the concept of moles. Here are the steps to find the pressure of hydrogen gas in the given scenario:

### Step 1: Calculate the number of moles of Carbon Dioxide (CO₂)
The molar mass of carbon dioxide (CO₂) is approximately 44 g/mol. Given that we have 44 g of CO₂:

\[ \text{Number of moles of CO₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{44 \text{ g}}{44 \text{ g/mol}} = 1 \text{ mole} \]

### Step 2: Use the Ideal Gas Law
We know that for an ideal gas, the pressure (P), volume (V), number of moles (n), and temperature (T) are related by the ideal gas equation:

\[ PV = nRT \]

Since both gases are in identical vessels at the same temperature, we can compare their pressures directly based on the number of moles.

### Step 3: Calculate the number of moles of Hydrogen (H₂)
The molar mass of hydrogen (H₂) is approximately 2 g/mol. Given that we have 44 g of H₂:

\[ \text{Number of moles of H₂} = \frac{44 \text{ g}}{2 \text{ g/mol}} = 22 \text{ moles} \]

### Step 4: Relate the pressures of the two gases
Since we know the pressure of CO₂ is 2 atm and it has 1 mole, we can set up a ratio to find the pressure of hydrogen. The pressure exerted by a gas is directly proportional to the number of moles when the volume and temperature are constant.

Let \( P_{H_2} \) be the pressure of hydrogen. We can set up the following relationship:

\[ \frac{P_{CO₂}}{P_{H₂}} = \frac{n_{CO₂}}{n_{H₂}} \]

Substituting the known values:

\[ \frac{2 \text{ atm}}{P_{H₂}} = \frac{1 \text{ mole}}{22 \text{ moles}} \]

### Step 5: Solve for the pressure of Hydrogen (H₂)
Rearranging the equation gives us:

\[ P_{H₂} = 2 \text{ atm} \times \frac{22 \text{ moles}}{1 \text{ mole}} = 44 \text{ atm} \]

### Final Answer
The pressure of hydrogen is 44 atm.

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