Rearrange the following `(I ` to `IV)` in the order of increasing masses `:`
(I) `0.5` mole of `O_(3)" "(II) 0.5 gm` atom of oxygen
(III) `3.011 xx 10^(23)` molecules of `O_(2) " " (IV) 5.6` litre of `CO_(2)` at `STP`

Options

A. `IIltIVlt III lt I`
B. `IIltIlt IV lt III`
C. `IV lt II ltIII ltI`
D. `Ilt II lt III lt IV`

Answer

To solve the problem of rearranging the given options in the order of increasing masses, we will calculate the mass of each option step by step.

### Step 1: Calculate the mass of 0.5 mole of O3
1. **Find the molar mass of O3**:
- The molar mass of oxygen (O) = 16 g/mol.
- Therefore, the molar mass of O3 = 3 × 16 g/mol = 48 g/mol.

2. **Calculate the mass for 0.5 mole**:
- Mass of 0.5 mole of O3 = 0.5 × 48 g = 24 g.

### Step 2: Calculate the mass of 0.5 gram atom of oxygen
1. **Understand what a gram atom means**:
- 1 gram atom of oxygen = 16 g (since it is the molar mass).

2. **Calculate the mass for 0.5 gram atom**:
- Mass of 0.5 gram atom of oxygen = 0.5 × 16 g = 8 g.

### Step 3: Calculate the mass of 3.011 × 10^23 molecules of O2
1. **Find the molar mass of O2**:
- The molar mass of O2 = 2 × 16 g/mol = 32 g/mol.

2. **Use Avogadro's number**:
- 1 mole of O2 = 6.022 × 10^23 molecules.

3. **Calculate the mass for 3.011 × 10^23 molecules**:
- Mass = (3.011 × 10^23 / 6.022 × 10^23) × 32 g = (0.5) × 32 g = 16 g.

### Step 4: Calculate the mass of 5.6 liters of CO2 at STP
1. **Understand the volume of gas at STP**:
- At STP, 22.4 liters of any gas occupies 1 mole.
- The molar mass of CO2 = 12 (C) + 2 × 16 (O) = 44 g/mol.

2. **Calculate the mass for 5.6 liters**:
- Mass = (5.6 liters / 22.4 liters) × 44 g = (0.25) × 44 g = 11 g.

### Summary of Masses
- (I) 0.5 mole of O3 = 24 g
- (II) 0.5 gram atom of oxygen = 8 g
- (III) 3.011 × 10^23 molecules of O2 = 16 g
- (IV) 5.6 liters of CO2 at STP = 11 g

### Step 5: Arrange in increasing order of mass
- The increasing order of masses is:
- (II) 0.5 gram atom of oxygen = 8 g
- (IV) 5.6 liters of CO2 at STP = 11 g
- (III) 3.011 × 10^23 molecules of O2 = 16 g
- (I) 0.5 mole of O3 = 24 g

### Final Answer
The order of increasing masses is:
(II) < (IV) < (III) < (I)

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