The density of liquid mercury is `13.6 g//cm^(3).` How many moles of mercury are there in 1 litre of the metal? (Atomic mass of `Hg=200).`

Explanation

To solve the problem, we need to determine how many moles of mercury are present in 1 liter of the metal, given its density and atomic mass. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Density of mercury (Hg) = 13.6 g/cm³
- Volume of mercury = 1 liter = 1000 mL
- Atomic mass of mercury (Hg) = 200 g/mol

### Step 2: Convert volume from liters to cubic centimeters
1 liter is equivalent to 1000 mL, and since 1 mL is equal to 1 cm³, we have:
\[ 1 \text{ L} = 1000 \text{ cm}^3 \]

### Step 3: Calculate the mass of mercury in 1 liter
Using the density formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
We can rearrange this to find mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Substituting the values:
\[ \text{Mass} = 13.6 \text{ g/cm}^3 \times 1000 \text{ cm}^3 = 13600 \text{ g} \]

### Step 4: Calculate the number of moles of mercury
Using the formula for moles:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]
Substituting the values:
\[ \text{Moles} = \frac{13600 \text{ g}}{200 \text{ g/mol}} = 68 \text{ moles} \]

### Conclusion
The number of moles of mercury in 1 liter of the metal is **68 moles**.

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