If 224 mL of triatomic gas has a mass of 1 g at 273 K and 1 atm. Pressure, then the mass of one atom is

Options

A. `8.30xx10^(-23)`g
B. `6.24xx10^(-23)`g
C. `2.08xx10^(-23)`g
D. `5.54xx10^(-23)`g

Explanation

To find the mass of one atom of a triatomic gas given that 224 mL of it has a mass of 1 g at 273 K and 1 atm, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Number of Moles of the Gas:**
- We know that at standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 L (or 22400 mL).
- Given volume of gas = 224 mL.
- Number of moles (n) = Volume of gas (mL) / Molar volume at STP (mL)
\[ n = \frac{224 \text{ mL}}{22400 \text{ mL/mol}} = \frac{1}{100} = 0.01 \text{ moles} \]

**Hint:** Remember that at STP, 1 mole of gas occupies 22.4 L or 22400 mL.

2. **Calculate the Number of Molecules:**
- Using Avogadro's number, \( N_A = 6.022 \times 10^{23} \) molecules/mol.
- Number of molecules = Number of moles × Avogadro's number
\[ \text{Number of molecules} = 0.01 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} = 6.022 \times 10^{21} \text{ molecules} \]

**Hint:** Avogadro's number helps convert moles to molecules.

3. **Calculate the Total Number of Atoms:**
- Since the gas is triatomic, each molecule contains 3 atoms.
- Total number of atoms = Number of molecules × 3
\[ \text{Total number of atoms} = 6.022 \times 10^{21} \text{ molecules} \times 3 = 1.8066 \times 10^{22} \text{ atoms} \]

**Hint:** Multiply the number of molecules by the number of atoms per molecule to find the total number of atoms.

4. **Calculate the Mass of One Atom:**
- The total mass of the gas is given as 1 g.
- The mass of one atom = Total mass / Total number of atoms
\[ \text{Mass of one atom} = \frac{1 \text{ g}}{1.8066 \times 10^{22} \text{ atoms}} \approx 5.54 \times 10^{-23} \text{ g} \]

**Hint:** To find the mass of one atom, divide the total mass by the total number of atoms.

### Final Answer:
The mass of one atom of the triatomic gas is approximately \( 5.54 \times 10^{-23} \) grams.