One mole of element X has 0.444 times the mass of one mole of element Y. One atom of element X has `2.96 times` the mass of one atom of `.^(12)C` . What is the atomic mass of Y ?

Options

A. 80
B. 15.77
C. 46.67
D. 40

Answer

To find the atomic mass of element Y based on the information given about elements X and Y, we can follow these steps:

### Step 1: Determine the mass of one mole of element X
We know that one atom of element X has a mass that is 2.96 times the mass of one atom of carbon-12. The atomic mass of carbon-12 is 12 g/mol.

\[ \text{Mass of one atom of X} = 2.96 \times \text{mass of one atom of } ^{12}C = 2.96 \times 12 \, \text{g/mol} \]

Calculating this gives:

\[ \text{Mass of one atom of X} = 2.96 \times 12 = 35.52 \, \text{g/mol} \]

### Step 2: Relate the mass of element X to the mass of element Y
According to the problem, one mole of element X has a mass that is 0.444 times the mass of one mole of element Y. We can express this relationship mathematically:

\[ \text{Mass of one mole of X} = 0.444 \times \text{Mass of one mole of Y} \]

### Step 3: Solve for the mass of one mole of element Y
From the previous step, we can rearrange the equation to find the mass of one mole of element Y:

\[ \text{Mass of one mole of Y} = \frac{\text{Mass of one mole of X}}{0.444} \]

Substituting the mass of one mole of X we calculated:

\[ \text{Mass of one mole of Y} = \frac{35.52 \, \text{g/mol}}{0.444} \]

Calculating this gives:

\[ \text{Mass of one mole of Y} \approx 80.72 \, \text{g/mol} \]

### Conclusion
The atomic mass of element Y is approximately **80.72 g/mol**.

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