Brine has a density of 1.2 g/cc. 40 cc of it are mixed with 30 cc of water. The density of solution is

Options

A. 2.11 g/cc
B. 1.11g/cc
C. 12.2g/cc
D. 20.4g/cc

Answer

To find the density of the solution formed by mixing 40 cc of brine with 30 cc of water, we can follow these steps:

### Step 1: Identify the densities and volumes
- Density of brine (D1) = 1.2 g/cc
- Volume of brine (V1) = 40 cc
- Density of water (D2) = 1 g/cc (standard density of water)
- Volume of water (V2) = 30 cc

### Step 2: Calculate the mass of brine
To find the mass of the brine, we use the formula:
\[ \text{Mass of brine} = \text{Density of brine} \times \text{Volume of brine} \]
\[ \text{Mass of brine} = D1 \times V1 = 1.2 \, \text{g/cc} \times 40 \, \text{cc} = 48 \, \text{g} \]

### Step 3: Calculate the mass of water
To find the mass of the water, we use the formula:
\[ \text{Mass of water} = \text{Density of water} \times \text{Volume of water} \]
\[ \text{Mass of water} = D2 \times V2 = 1 \, \text{g/cc} \times 30 \, \text{cc} = 30 \, \text{g} \]

### Step 4: Calculate the total mass of the solution
Now, we add the masses of the brine and water to find the total mass of the solution:
\[ \text{Total mass} = \text{Mass of brine} + \text{Mass of water} \]
\[ \text{Total mass} = 48 \, \text{g} + 30 \, \text{g} = 78 \, \text{g} \]

### Step 5: Calculate the total volume of the solution
Next, we find the total volume of the solution by adding the volumes of brine and water:
\[ \text{Total volume} = V1 + V2 = 40 \, \text{cc} + 30 \, \text{cc} = 70 \, \text{cc} \]

### Step 6: Calculate the density of the solution
Finally, we calculate the density of the solution using the formula:
\[ \text{Density of solution} = \frac{\text{Total mass}}{\text{Total volume}} \]
\[ \text{Density of solution} = \frac{78 \, \text{g}}{70 \, \text{cc}} \approx 1.11 \, \text{g/cc} \]

### Final Answer
The density of the solution is approximately **1.11 g/cc**.

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