Calculate the molarity of a solution of 30 g of `Co(NO_(3))_(2).6H_(2)O` in 4.3 L of solution? Consider atomic mass of Co = 59u, N - 14u, O = 16u, H = lu.

Options

A. 0.023 M
B. 0.23 M
C. 0.046 M
D. 0.46 M

Explanation

To calculate the molarity of a solution of 30 g of `Co(NO₃)₂.6H₂O` in 4.3 L of solution, we will follow these steps:

### Step 1: Calculate the Molecular Weight of `Co(NO₃)₂.6H₂O`

1. **Identify the components of the compound:**
- Cobalt (Co)
- Nitrogen (N)
- Oxygen (O)
- Water (H₂O)

2. **Calculate the molecular weight using the atomic masses:**
- Atomic mass of Co = 59 u
- Atomic mass of N = 14 u
- Atomic mass of O = 16 u
- Atomic mass of H = 1 u

3. **Molecular weight calculation:**
- For `Co`: 1 × 59 = 59 u
- For `N`: 2 × 14 = 28 u (since there are 2 nitrate ions)
- For `O`: 6 × 16 = 96 u (from the 6 oxygen atoms in the nitrate ions)
- For `H₂O`: 6 × (2 × 1 + 16) = 6 × 18 = 108 u (from the 6 water molecules)

4. **Total molecular weight:**
\[ \text{Molecular weight} = 59 + 28 + 96 + 108 = 291 \text{ u} \]

### Step 2: Calculate the Number of Moles of `Co(NO₃)₂.6H₂O`

1. **Use the formula for moles:**
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molecular weight}} \]
- Given weight = 30 g
- Molecular weight = 291 g/mol

2. **Calculate the number of moles:**
\[ \text{Number of moles} = \frac{30 \text{ g}}{291 \text{ g/mol}} \approx 0.1029 \text{ moles} \]

### Step 3: Calculate Molarity

1. **Use the formula for molarity:**
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
- Volume of solution = 4.3 L

2. **Calculate molarity:**
\[ \text{Molarity} = \frac{0.1029 \text{ moles}}{4.3 \text{ L}} \approx 0.0239 \text{ M} \]

### Final Answer

The molarity of the solution is approximately **0.0239 M**.

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