A rigid tank contains `35 kg` of nitrogen at `6` atm. Sufficient quantity of oxygen is supplied to increase the pressure to `9` atm, while the temperature reamins constant. Amount of oxygen supplied to the tank is:

Options

A. `5 kg`
B. `10 kg`
C. `20 kg`
D. `40 kg`

Explanation

To solve the problem step by step, we will use the ideal gas law and the relationship between pressure, volume, and the number of moles of gas.

### Step 1: Identify the initial conditions
We have a rigid tank containing nitrogen gas with the following properties:
- Mass of nitrogen (N₂) = 35 kg
- Initial pressure (P₁) = 6 atm

### Step 2: Calculate the number of moles of nitrogen
To find the number of moles (N₁) of nitrogen, we use the formula:
\[ N = \frac{m}{M} \]
where \( m \) is the mass of the gas and \( M \) is the molar mass.

The molar mass of nitrogen (N₂) is approximately 28 g/mol. First, convert the mass from kg to grams:
\[ m = 35 \, \text{kg} = 35 \times 10^3 \, \text{g} = 35000 \, \text{g} \]
Now, calculate the number of moles:
\[ N₁ = \frac{35000 \, \text{g}}{28 \, \text{g/mol}} = 1250 \, \text{moles} \]

### Step 3: Use the ideal gas law to relate the pressures and moles
Since the volume and temperature are constant, we can use the relationship between pressure and the number of moles:
\[ \frac{P₁}{P₂} = \frac{N₁}{N} \]
where \( N \) is the total number of moles after adding oxygen.

Given:
- Final pressure (P₂) = 9 atm

Rearranging the equation gives:
\[ N = \frac{P₂}{P₁} \times N₁ \]

### Step 4: Calculate the total number of moles after adding oxygen
Substituting the known values:
\[ N = \frac{9 \, \text{atm}}{6 \, \text{atm}} \times 1250 \, \text{moles} = 1.5 \times 1250 = 1875 \, \text{moles} \]

### Step 5: Calculate the number of moles of oxygen added
The number of moles of oxygen (N₂) supplied is:
\[ N₂ = N - N₁ = 1875 \, \text{moles} - 1250 \, \text{moles} = 625 \, \text{moles} \]

### Step 6: Calculate the mass of oxygen supplied
The molar mass of oxygen (O₂) is approximately 32 g/mol. To find the mass of oxygen supplied, we use:
\[ \text{Mass} = N₂ \times M \]
Substituting the values:
\[ \text{Mass} = 625 \, \text{moles} \times 32 \, \text{g/mol} = 20000 \, \text{g} = 20 \, \text{kg} \]

### Final Answer
The amount of oxygen supplied to the tank is **20 kg**.

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