2g of `H_2` and 17g of `NH_3` are placed in a 8.21 litre flask at `27^@C`. The total pressure of the gas mixture is?

Options

A. 4 atm
B. 5 atm
C. 6 atm
D. 3 atm.

Explanation

To find the total pressure of the gas mixture in the flask, we can follow these steps:

### Step 1: Calculate the number of moles of each gas.

1. **For Hydrogen (H₂)**:
- Given mass of H₂ = 2 g
- Molar mass of H₂ = 2 g/mol
- Number of moles (n) = mass / molar mass = 2 g / 2 g/mol = 1 mole

2. **For Ammonia (NH₃)**:
- Given mass of NH₃ = 17 g
- Molar mass of NH₃ = 14 (N) + 3 (H) = 17 g/mol
- Number of moles (n) = mass / molar mass = 17 g / 17 g/mol = 1 mole

### Step 2: Calculate the total number of moles of the gas mixture.

- Total moles = moles of H₂ + moles of NH₃ = 1 mole + 1 mole = 2 moles

### Step 3: Use the Ideal Gas Law to find the total pressure.

The Ideal Gas Law is given by the equation:
\[ PV = nRT \]
Where:
- P = pressure (in atm)
- V = volume (in liters)
- n = number of moles
- R = universal gas constant = 0.0821 L·atm/(K·mol)
- T = temperature in Kelvin

1. **Convert the temperature from Celsius to Kelvin**:
- Given temperature = 27°C
- T(K) = 27 + 273 = 300 K

2. **Substitute the known values into the Ideal Gas Law**:
- V = 8.21 L
- n = 2 moles
- R = 0.0821 L·atm/(K·mol)
- T = 300 K

\[ P \times 8.21 = 2 \times 0.0821 \times 300 \]

### Step 4: Solve for P (pressure).

1. Calculate the right-hand side:
\[ 2 \times 0.0821 \times 300 = 49.26 \]

2. Now, solve for P:
\[ P = \frac{49.26}{8.21} \]
\[ P \approx 6.00 \text{ atm} \]

### Final Answer:
The total pressure of the gas mixture is approximately **6 atm**.

---