Calculate the concentration of a solution of sodium chloride, which was made by dissolving 1.16 g of solid sodium chloride in water and making the solution up to 250 cm. (Atomic mass of Na = 23 u, Cl = 35 u)

Options

A. `"2 mol dm"^(-3)`
B. `"0.04 mol cm"^(-3)`
C. `"0.08 mol dm"^(-3)`
D. `"0.02 mol cm"^(-3)`

Answer

To calculate the concentration (molarity) of the sodium chloride (NaCl) solution, we will follow these steps:

### Step 1: Calculate the Molar Mass of Sodium Chloride (NaCl)
- The atomic mass of Sodium (Na) = 23 u
- The atomic mass of Chlorine (Cl) = 35.5 u
- Molar mass of NaCl = Atomic mass of Na + Atomic mass of Cl
\[ \text{Molar mass of NaCl} = 23 + 35.5 = 58.5 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of Sodium Chloride
- Use the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass of solute (g)}}{\text{molar mass (g/mol)}} \]
- Given mass of NaCl = 1.16 g
\[ \text{Number of moles} = \frac{1.16 \text{ g}}{58.5 \text{ g/mol}} \approx 0.0198 \text{ moles} \]

### Step 3: Convert the Volume of the Solution from cm³ to Liters
- Since molarity is expressed in moles per liter, convert the volume:
\[ 250 \text{ cm}^3 = 250 \text{ mL} = 0.250 \text{ L} \]

### Step 4: Calculate the Molarity of the Solution
- Use the formula for molarity:
\[ \text{Molarity (M)} = \frac{\text{number of moles}}{\text{volume of solution in liters}} \]
- Substitute the values:
\[ \text{Molarity} = \frac{0.0198 \text{ moles}}{0.250 \text{ L}} \approx 0.0792 \text{ M} \]

### Final Answer
The concentration of the sodium chloride solution is approximately **0.0792 M**.

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