Weight of `6.022 xx 10^(20)` atoms of silver (at. mass 108 u) is

Options

A. `108 xx 10^(3)g `
B. 108 g
C. 0.108 g
D. 10.8 g

Explanation

To find the weight of \(6.022 \times 10^{20}\) atoms of silver (with an atomic mass of 108 u), we can follow these steps:

### Step 1: Understand the relationship between moles and atoms
1 mole of any substance contains \(6.022 \times 10^{23}\) entities (atoms, molecules, etc.). This number is known as Avogadro's number.

### Step 2: Determine the weight of 1 mole of silver
The atomic mass of silver is given as 108 u, which means that 1 mole of silver weighs 108 grams.

### Step 3: Set up the proportion to find the weight of \(6.022 \times 10^{20}\) atoms
We need to find the weight of \(6.022 \times 10^{20}\) atoms of silver. We can set up the following proportion based on the number of atoms:

\[ \text{Weight of } 6.022 \times 10^{20} \text{ atoms} = \left(\frac{108 \text{ grams}}{6.022 \times 10^{23} \text{ atoms}}\right) \times 6.022 \times 10^{20} \text{ atoms} \]

### Step 4: Calculate the weight
Now, we can perform the calculation:

\[ \text{Weight} = \frac{108 \text{ grams}}{6.022 \times 10^{23}} \times 6.022 \times 10^{20} \]

### Step 5: Simplify the expression
The \(6.022\) terms will cancel out, and we can simplify the expression:

\[ \text{Weight} = 108 \text{ grams} \times \frac{6.022 \times 10^{20}}{6.022 \times 10^{23}} = 108 \text{ grams} \times 10^{-3} \]

### Step 6: Final calculation
Now, we can calculate:

\[ \text{Weight} = 0.108 \text{ grams} \]

### Final Answer
The weight of \(6.022 \times 10^{20}\) atoms of silver is **0.108 grams**.

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