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 solve the problem, we need to find the molecular weight of substance X given the number of molecules of X and Y, the weight of the mixture, and the molecular weight of Y.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- 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 = 0.688 g
- Molecular weight of Y = 187 g/mol

2. **Calculate the Mass of Y:**
- First, we need to find the mass of Y using the number of molecules.
- We know that 1 mole of any substance contains \(6.022 \times 10^{23}\) molecules (Avogadro's number).
- Therefore, the mass of Y can be calculated using the formula:
\[ \text{Mass of Y} = \left(\frac{\text{Number of molecules of Y}}{6.022 \times 10^{23}}\right) \times \text{Molecular weight of Y} \]
- Plugging in the values:
\[ \text{Mass of Y} = \left(\frac{1.85 \times 10^{21}}{6.022 \times 10^{23}}\right) \times 187 \]
- Calculating this gives:
\[ \text{Mass of Y} = \left(3.07 \times 10^{-3}\right) \times 187 \approx 0.574 \text{ g} \]

3. **Calculate the Mass of X:**
- Now, we can find the mass of X by subtracting the mass of Y from the total mass of the mixture:
\[ \text{Mass of X} = \text{Total mass} - \text{Mass of Y} \]
- Plugging in the values:
\[ \text{Mass of X} = 0.688 \text{ g} - 0.574 \text{ g} = 0.114 \text{ g} \]

4. **Calculate the Molecular Weight of X:**
- Now we will calculate the molecular weight of X using the mass of X and the number of molecules of X:
- Using the formula:
\[ \text{Molecular weight of X} = \left(\frac{\text{Mass of X}}{\text{Number of molecules of X}/6.022 \times 10^{23}}\right) \]
- Plugging in the values:
\[ \text{Molecular weight of X} = \left(\frac{0.114 \text{ g}}{1.65 \times 10^{21}/6.022 \times 10^{23}}\right) \]
- Calculating this gives:
\[ \text{Molecular weight of X} = \left(\frac{0.114 \text{ g}}{2.743 \times 10^{-3}}\right) \approx 41.6 \text{ g/mol} \]

### Final Answer:
The molecular weight of X is approximately **41.6 g/mol**.