The mass of a molecule of carbon-14 dioxide `(""^(14)CO_(2))` is g.

Answer

To find the mass of a molecule of carbon-14 dioxide (C-14O2), we can follow these steps:

### Step 1: Determine the molecular weight of carbon-14 dioxide (C-14O2).
- The molecular formula for carbon dioxide is CO2, which consists of one carbon atom and two oxygen atoms.
- The atomic weight of carbon-14 (C-14) is 14 g/mol.
- The atomic weight of oxygen (O) is 16 g/mol. Since there are two oxygen atoms, we multiply this by 2.

**Calculation:**
- Molecular weight of C-14O2 = Atomic weight of C-14 + 2 × Atomic weight of O
- Molecular weight of C-14O2 = 14 g/mol + 2 × 16 g/mol
- Molecular weight of C-14O2 = 14 g/mol + 32 g/mol = 46 g/mol

### Step 2: Use Avogadro's number to find the number of molecules in 46 grams of C-14O2.
- Avogadro's number (N_A) is approximately 6.022 × 10^23 molecules/mol.
- This means that 46 grams of C-14O2 contains 6.022 × 10^23 molecules.

### Step 3: Calculate the mass of a single molecule of C-14O2.
- To find the mass of one molecule, we can divide the total mass of the substance by the number of molecules.

**Calculation:**
- Mass of one molecule of C-14O2 = Total mass / Number of molecules
- Mass of one molecule of C-14O2 = 46 g / (6.022 × 10^23 molecules)
- Mass of one molecule of C-14O2 = 7.637 × 10^-23 g

### Final Answer:
The mass of a molecule of carbon-14 dioxide (C-14O2) is approximately **7.637 × 10^-23 grams**.

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