Cisplatin, an anticancer drug, has the molecular formula `Pt(NH_3)_2 Cl_2.` What is the mass (in gram) of one molecule ? (Atomic masses : `Pt=195, H=14, Cl=35.5`)

Options

A. `4.98xx10^(23)`
B. `1.08xx10^(-22)`
C. `6.55xx10^(-21)`
D. `3.85xx10^(-22)`

Answer

To find the mass of one molecule of cisplatin (Pt(NH₃)₂Cl₂), we will follow these steps:

### Step 1: Determine the molar mass of cisplatin
We will calculate the molar mass by adding the atomic masses of all the atoms in the molecular formula.

- **Platinum (Pt)**: 1 atom × 195 g/mol = 195 g/mol
- **Nitrogen (N)**: 2 atoms × 14 g/mol = 28 g/mol
- **Hydrogen (H)**: 6 atoms (from 2 NH₃) × 1 g/mol = 6 g/mol
- **Chlorine (Cl)**: 2 atoms × 35.5 g/mol = 71 g/mol

Now, we add these values together:
\[ \text{Molar mass of cisplatin} = 195 + 28 + 6 + 71 = 300 \text{ g/mol} \]

### Step 2: Calculate the mass of one molecule
We know that 1 mole of any substance contains \(6.022 \times 10^{23}\) molecules (Avogadro's number). Therefore, the mass of one molecule can be calculated using the molar mass.

\[ \text{Mass of one molecule} = \frac{\text{Molar mass}}{\text{Avogadro's number}} = \frac{300 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \]

### Step 3: Perform the calculation
Now we will perform the division:
\[ \text{Mass of one molecule} = \frac{300}{6.022 \times 10^{23}} \approx 4.98 \times 10^{-22} \text{ g} \]

### Final Answer
The mass of one molecule of cisplatin is approximately \(4.98 \times 10^{-22}\) grams.

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