A solution contains 40 g of common salt in 320 g of water. What is the concentration of the solution in terms of mass by mass percentage?
11.1%
Calculating Solution Concentration: Mass by Mass Percentage
This solution explains how to determine the concentration of a solution using the mass by mass percentage method. We will analyze the given quantities of solute and solvent to find the solution's concentration.
Understanding Mass by Mass Percentage
The concentration of a solution expressed as mass by mass percentage (often denoted as %(w/w)) indicates the mass of the solute present in every 100 units of mass of the solution. It's calculated using the formula:
\( \text{Concentration (mass by mass \%)} = \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \times 100\% \)
Key terms used:
- Solute: The substance that gets dissolved. Here, it is common salt.
- Solvent: The substance that does the dissolving. Here, it is water.
- Solution: The uniform mixture formed when a solute dissolves in a solvent.
- Mass of Solution: The total mass of the mixture, calculated by adding the mass of the solute and the mass of the solvent.
Given Information
The problem provides the following details:
- Mass of Solute (common salt) = 40 g
- Mass of Solvent (water) = 320 g
Step-by-Step Calculation
To find the mass by mass percentage, follow these steps:
-
Calculate the Mass of the Solution:
Add the mass of the solute and the mass of the solvent to get the total mass of the solution.
\( \text{Mass of Solution} = \text{Mass of Solute} + \text{Mass of Solvent} \)
\( \text{Mass of Solution} = 40 \, \text{g} + 320 \, \text{g} \)
\( \text{Mass of Solution} = 360 \, \text{g} \)
-
Calculate the Mass by Mass Percentage Concentration:
Use the concentration formula with the calculated mass of the solution.
\( \text{Concentration (mass by mass \%)} = \frac{\text{Mass of Solute}}{\text{Mass of Solution}} \times 100\% \)
Substitute the known values:\( \text{Concentration} = \frac{40 \, \text{g}}{360 \, \text{g}} \times 100\% \)
Simplify the fraction:\( \text{Concentration} = \frac{4}{36} \times 100\% \)
\( \text{Concentration} = \frac{1}{9} \times 100\% \)
Perform the final calculation:\( \text{Concentration} \approx 11.11\% \)
Final Result Interpretation
The calculated concentration is approximately 11.11%. This value represents the mass of common salt dissolved in 100 g of the solution. The closest option matches this calculated value.
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