Sure, let's solve this problem step-by-step.
1. Understanding the Problem:
- We are given 40 grams of sugar.
- We are given 100 grams of water.
- We need to find the concentration of the solution in terms of mass by mass percentage.
2. Calculate the Total Mass of the Solution:
- Total mass is the sum of the mass of sugar and the mass of water.
- Total mass = mass of sugar + mass of water
- Total mass = 40 gm (sugar) + 100 gm (water)
- Total mass = 140 gm
3. Calculate the Concentration:
- The concentration in terms of mass by mass percentage is given by the formula:
[tex]\[
\text{Concentration (\%)} = \left(\frac{\text{mass of solute}}{\text{total mass of solution}}\right) \times 100
\][/tex]
- Here, the mass of the solute (sugar) is 40 gm, and the total mass of the solution is 140 gm.
- Substituting the values into the formula:
[tex]\[
\text{Concentration (\%)} = \left(\frac{40 \text{ gm}}{140 \text{ gm}}\right) \times 100
\][/tex]
- Performing the division first:
[tex]\[
\frac{40}{140} \approx 0.2857142857
\][/tex]
- Multiplying by 100 to get the percentage:
[tex]\[
0.2857142857 \times 100 = 28.57142857142857
\][/tex]
So, the concentration of the solution in terms of mass by mass percentage is approximately 28.57%.
