40% by weight solution will contain how much mass of the solute in 1 solution, density of the solution is 1.2 g/mL

Options

A. 480 g
B. 48 g
C. 38 g
D. 380 g

Explanation

To solve the problem of how much mass of solute is contained in a 40% by weight solution with a density of 1.2 g/mL, we can follow these steps:

### Step 1: Understand the Definition of a 40% by Weight Solution
A 40% by weight solution means that there are 40 grams of solute for every 100 grams of solution.

### Step 2: Calculate the Mass of the Solution
Let's assume we have 100 grams of the solution. Since it is a 40% by weight solution, the mass of the solute (let's denote it as \( m_{solute} \)) can be calculated as follows:
\[ m_{solute} = 40\% \times 100 \text{ g} = 40 \text{ g} \]

### Step 3: Calculate the Mass of the Solvent
The mass of the solvent (let's denote it as \( m_{solvent} \)) can be calculated as:
\[ m_{solvent} = 100 \text{ g} - m_{solute} = 100 \text{ g} - 40 \text{ g} = 60 \text{ g} \]

### Step 4: Calculate the Volume of the Solution
We need to find the volume of the solution. The density of the solution is given as 1.2 g/mL. We can use the formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Rearranging the formula to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1.2 \text{ g/mL}} \approx 83.33 \text{ mL} \]

### Step 5: Calculate the Molarity of the Solution
Molarity (M) is defined as the number of moles of solute per liter of solution. First, we need to convert the mass of the solute into moles. To do this, we need the molar mass of the solute. Let's assume the solute is a common one like sodium chloride (NaCl) with a molar mass of approximately 58.44 g/mol.

Calculating the number of moles of solute:
\[ \text{Number of moles} = \frac{m_{solute}}{\text{Molar mass}} = \frac{40 \text{ g}}{58.44 \text{ g/mol}} \approx 0.684 \text{ moles} \]

Now, we convert the volume from mL to L:
\[ \text{Volume in L} = \frac{83.33 \text{ mL}}{1000} = 0.08333 \text{ L} \]

Now we can calculate the molarity:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{0.684 \text{ moles}}{0.08333 \text{ L}} \approx 8.21 \text{ M} \]

### Final Result
The mass of the solute in a 40% by weight solution is 40 grams.

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