What is the mass of 2L of `N_2 ` at 22.4 atm pressure and 273K

Options

A. 28 g
B. ` 14 xx 224g`
C. ` 56g`
D. ` 15g`

Explanation

To find the mass of 2 liters of nitrogen gas (N₂) at a pressure of 22.4 atm and a temperature of 273 K, we can use the ideal gas law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature (in Kelvin)

### Step 1: Identify the known values
- Pressure, \( P = 22.4 \) atm
- Volume, \( V = 2 \) L
- Temperature, \( T = 273 \) K
- Ideal gas constant, \( R = 0.0821 \) L·atm/(K·mol)

### Step 2: Rearrange the ideal gas law to solve for \( n \)
We need to find the number of moles \( n \):
\[ n = \frac{PV}{RT} \]

### Step 3: Substitute the known values into the equation
Now we substitute the values into the equation:
\[ n = \frac{(22.4 \, \text{atm}) \times (2 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (273 \, \text{K})} \]

### Step 4: Calculate the value of \( n \)
Calculating the denominator:
\[ 0.0821 \times 273 \approx 22.4143 \]

Now substituting back into the equation:
\[ n = \frac{44.8}{22.4143} \approx 2 \, \text{moles} \]

### Step 5: Calculate the mass of N₂
The molar mass of nitrogen gas (N₂) is approximately 28 g/mol. To find the mass, we multiply the number of moles by the molar mass:
\[ \text{Mass} = n \times \text{molar mass} = 2 \, \text{moles} \times 28 \, \text{g/mol} = 56 \, \text{grams} \]

### Final Answer
The mass of 2 liters of N₂ at 22.4 atm pressure and 273 K is **56 grams**.

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