Rahul Dravid wants to wear `6.023xx10^(21)` Ag atms in the form of a ring. His Silver Gold Copper alloy ring consists of 20% of Silver. The mass of the ring is 0.9 x. What is x?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the number of moles of silver required
Rahul Dravid wants to wear \(6.023 \times 10^{21}\) Ag atoms. To find the number of moles of silver, we use Avogadro's number, which is \(6.023 \times 10^{23}\) atoms/mole.

\[ \text{Number of moles of silver} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} = \frac{6.023 \times 10^{21}}{6.023 \times 10^{23}} = 0.01 \text{ moles} \]

### Step 2: Calculate the total mass of silver in the ring
The ring is made of an alloy that contains 20% silver. The total mass of the ring is given as \(0.9x\). Therefore, the mass of silver in the ring can be calculated as:

\[ \text{Mass of silver} = 20\% \text{ of total mass} = 0.2 \times (0.9x) = 0.18x \]

### Step 3: Calculate the number of moles of silver in the ring
The number of moles of silver can also be calculated using its mass and molar mass. The atomic mass of silver (Ag) is 108 g/mol. Therefore, the number of moles of silver in the ring is:

\[ \text{Number of moles of silver} = \frac{\text{Mass of silver}}{\text{Molar mass of silver}} = \frac{0.18x}{108} \]

### Step 4: Set up the equation
Since we know from Step 1 that the number of moles of silver required is 0.01 moles, we can set up the equation:

\[ \frac{0.18x}{108} = 0.01 \]

### Step 5: Solve for \(x\)
Now we can solve for \(x\):

\[ 0.18x = 0.01 \times 108 \]
\[ 0.18x = 1.08 \]
\[ x = \frac{1.08}{0.18} = 6 \]

### Conclusion
The value of \(x\) is \(6\).

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