Which one of the following has greater active mass

Options

A. 200g of lime stone in 2L vessel
B. 90g of `CS_2` liquid in 100ml vessel
C. 50g of `N_2` gas in 0.5L vessel
D. 1mole of `O_2` gas at STP

Explanation

To determine which substance has the greater active mass, we will calculate the active mass for each of the given options step by step. The active mass is defined as the concentration of a substance, which can be expressed in terms of moles per liter (Molarity).

### Step 1: Calculate the active mass for 200 gm of CaCO3 in a 2-liter vessel.

1. **Identify the formula for active mass**:
\[ \text{Active Mass} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]

2. **Calculate the molar mass of CaCO3**:
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (3 atoms)
\[ \text{Molar mass of CaCO3} = 40 + 12 + (16 \times 3) = 100 \text{ g/mol} \]

3. **Calculate the number of moles of CaCO3**:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{200 \text{ g}}{100 \text{ g/mol}} = 2 \text{ moles} \]

4. **Calculate the active mass**:
\[ \text{Active Mass} = \frac{2 \text{ moles}}{2 \text{ L}} = 1 \]

### Step 2: Calculate the active mass for 90 gm of CS2 in a 100 ml vessel.

1. **Convert volume from ml to liters**:
\[ 100 \text{ ml} = 0.1 \text{ L} \]

2. **Calculate the molar mass of CS2**:
- Carbon (C) = 12 g/mol
- Sulfur (S) = 32 g/mol (2 atoms)
\[ \text{Molar mass of CS2} = 12 + (32 \times 2) = 76 \text{ g/mol} \]

3. **Calculate the number of moles of CS2**:
\[ \text{Number of moles} = \frac{90 \text{ g}}{76 \text{ g/mol}} \approx 1.184 \text{ moles} \]

4. **Calculate the active mass**:
\[ \text{Active Mass} = \frac{1.184 \text{ moles}}{0.1 \text{ L}} = 11.84 \]

### Step 3: Calculate the active mass for 50 gm of N2 in a 0.5-liter vessel.

1. **Calculate the molar mass of N2**:
- Nitrogen (N) = 14 g/mol (2 atoms)
\[ \text{Molar mass of N2} = 14 \times 2 = 28 \text{ g/mol} \]

2. **Calculate the number of moles of N2**:
\[ \text{Number of moles} = \frac{50 \text{ g}}{28 \text{ g/mol}} \approx 1.785 \text{ moles} \]

3. **Calculate the active mass**:
\[ \text{Active Mass} = \frac{1.785 \text{ moles}}{0.5 \text{ L}} = 3.57 \]

### Step 4: Calculate the active mass for 1 mole of O2 gas at STP.

1. **At STP, the volume of 1 mole of gas is 22.4 L**.

2. **Calculate the active mass**:
\[ \text{Active Mass} = \frac{1 \text{ mole}}{22.4 \text{ L}} \approx 0.04464 \]

### Step 5: Compare the active masses calculated.

- Active mass of CaCO3: 1
- Active mass of CS2: 11.84
- Active mass of N2: 3.57
- Active mass of O2: 0.04464

### Conclusion:
The substance with the greatest active mass is **CS2** with an active mass of **11.84**.