If the mass of 0.25 moles of an element Xis 2.25g, the mass of one atom of X is about:

Options

A. `1.5 xx 10^(-24)`g
B. `2.5 xx 10^(-23)`g
C. `1.5 xx 10^(-23)`g
D. `2.5 xx 10^(-24)`g

Answer

To find the mass of one atom of element X, we can follow these steps:

### Step 1: Determine the mass of 1 mole of element X
Given that the mass of 0.25 moles of element X is 2.25 grams, we can find the mass of 1 mole by using the following calculation:

\[ \text{Mass of 1 mole} = \frac{\text{Mass of 0.25 moles}}{0.25} \]

Substituting the given values:

\[ \text{Mass of 1 mole} = \frac{2.25 \text{ g}}{0.25} = 9 \text{ g} \]

### Step 2: Use Avogadro's number to find the number of atoms in 1 mole
Avogadro's number states that 1 mole of any substance contains approximately \(6.022 \times 10^{23}\) atoms.

### Step 3: Calculate the mass of one atom of element X
To find the mass of one atom, we divide the mass of 1 mole by Avogadro's number:

\[ \text{Mass of 1 atom} = \frac{\text{Mass of 1 mole}}{\text{Avogadro's number}} \]

Substituting the values we have:

\[ \text{Mass of 1 atom} = \frac{9 \text{ g}}{6.022 \times 10^{23}} \]

### Step 4: Perform the calculation
Now, we calculate the mass of one atom:

\[ \text{Mass of 1 atom} \approx \frac{9}{6.022 \times 10^{23}} \approx 1.49 \times 10^{-23} \text{ g} \]

Rounding this to two significant figures, we get:

\[ \text{Mass of 1 atom} \approx 1.5 \times 10^{-23} \text{ g} \]

### Final Answer
The mass of one atom of element X is approximately \(1.5 \times 10^{-23}\) grams.

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