A mixture of `1.65 xx 10^(21)` molecules of X and `1.85 xx 10^(21)` molecules of Y weighs 0.688 g . The mol . wt . Of X is (Assume mol . wt . Of Y is 187)

Options

A. 52
B. 84
C. 126
D. 41.47

Answer

To find the molecular weight of substance X in the given mixture, we can follow these steps:

### Step 1: Write down the given information
- Number of molecules of X = \(1.65 \times 10^{21}\)
- Number of molecules of Y = \(1.85 \times 10^{21}\)
- Total weight of the mixture (X + Y) = 0.688 g
- Molecular weight of Y = 187 g/mol

### Step 2: Calculate the mass of substance Y
To find the mass of Y, we first need to determine the mass of one molecule of Y.

1. **Calculate the mass of one molecule of Y:**
\[ \text{Mass of one molecule of Y} = \frac{\text{Molecular weight of Y}}{N_A} = \frac{187 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \approx 3.11 \times 10^{-22} \text{ g} \]

2. **Calculate the total mass of Y:**
\[ \text{Mass of Y} = \text{Number of molecules of Y} \times \text{Mass of one molecule of Y} \]
\[ \text{Mass of Y} = 1.85 \times 10^{21} \text{ molecules} \times 3.11 \times 10^{-22} \text{ g/molecule} \approx 0.574 \text{ g} \]

### Step 3: Calculate the mass of substance X
Now that we have the mass of Y, we can find the mass of X.

\[ \text{Mass of X} = \text{Total mass} - \text{Mass of Y} \]
\[ \text{Mass of X} = 0.688 \text{ g} - 0.574 \text{ g} = 0.114 \text{ g} \]

### Step 4: Calculate the mass of one molecule of X
Now, we can find the mass of one molecule of X.

\[ \text{Mass of one molecule of X} = \frac{\text{Mass of X}}{\text{Number of molecules of X}} = \frac{0.114 \text{ g}}{1.65 \times 10^{21} \text{ molecules}} \approx 6.91 \times 10^{-23} \text{ g} \]

### Step 5: Calculate the mass of one mole of X
To find the mass of one mole of X, we multiply the mass of one molecule by Avogadro's number.

\[ \text{Mass of one mole of X} = \text{Mass of one molecule of X} \times N_A \]
\[ \text{Mass of one mole of X} = 6.91 \times 10^{-23} \text{ g} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 41.60 \text{ g} \]

### Step 6: Determine the molecular weight of X
The molecular weight of X is equal to the mass of one mole of X in grams.

\[ \text{Molecular weight of X} = 41.60 \text{ g/mol} \approx 42 \text{ g/mol} \]

### Final Answer
The molecular weight of X is approximately **42 g/mol**.

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