Worksheet on calculating concentration of solutions using percent by weight and volume methods.

Problem Set: Concentration of Solutions

We are tasked with solving problems related to the concentration of solutions using the GUESS method. The GUESS method involves:
1. Given: Identify what is given in the problem.
2. Unknown: Determine what you need to find.
3. Equation: Write down the relevant equation.
4. Substitute: Substitute the given values into the equation.
5. Solve: Solve for the unknown.

Let's solve each problem step by step.

---

Problem 1: Percent by mass of salt solution

#### Given:
- Mass of solute (salt) = 11 g
- Total mass of solution = 80 g

#### Unknown:
- Percent by mass (\% w/w)

#### Equation:
\[
\% \text{w/w} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\%
\]

#### Substitute:
\[
\% \text{w/w} = \frac{11 \, \text{g}}{80 \, \text{g}} \times 100\%
\]

#### Solve:
\[
\% \text{w/w} = \frac{11}{80} \times 100\% = 0.1375 \times 100\% = 13.75\%
\]

#### Answer:
\[
\boxed{13.75\%}
\]

---

Problem 2: Percent by mass concentration of sugar solution

#### Given:
- Mass of solute (sugar) = 8 g
- Mass of solvent (water) = 15 g

#### Unknown:
- Percent by mass (\% w/w)

#### Equation:
\[
\% \text{w/w} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\%
\]

#### Total mass of solution:
\[
\text{Total mass of solution} = \text{mass of solute} + \text{mass of solvent} = 8 \, \text{g} + 15 \, \text{g} = 23 \, \text{g}
\]

#### Substitute:
\[
\% \text{w/w} = \frac{8 \, \text{g}}{23 \, \text{g}} \times 100\%
\]

#### Solve:
\[
\% \text{w/w} = \frac{8}{23} \times 100\% \approx 0.3478 \times 100\% \approx 34.78\%
\]

#### Answer:
\[
\boxed{34.78\%}
\]

---

Problem 3: Grams of sodium chloride in a salt solution

#### Given:
- Volume of solution = 250 mL
- Percent by mass (\% w/w) of sodium chloride = 9%

#### Unknown:
- Mass of sodium chloride (solute)

#### Assumption:
The density of the solution is not provided, so we assume the volume of the solution is equivalent to its mass in grams (common assumption for dilute solutions). Therefore, the total mass of the solution is 250 g.

#### Equation:
\[
\% \text{w/w} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\%
\]

Rearrange to solve for the mass of solute:
\[
\text{mass of solute} = \frac{\% \text{w/w} \times \text{total mass of solution}}{100\%}
\]

#### Substitute:
\[
\text{mass of solute} = \frac{9\% \times 250 \, \text{g}}{100\%}
\]

#### Solve:
\[
\text{mass of solute} = \frac{9 \times 250}{100} = \frac{2250}{100} = 22.5 \, \text{g}
\]

#### Answer:
\[
\boxed{22.5 \, \text{g}}
\]

---

Problem 4: Percent by mass of brass alloy

#### Given:
- Mass of copper = 70 g
- Mass of zinc = 30 g

#### Unknown:
- Percent by mass of copper and zinc

#### Total mass of alloy:
\[
\text{Total mass of alloy} = \text{mass of copper} + \text{mass of zinc} = 70 \, \text{g} + 30 \, \text{g} = 100 \, \text{g}
\]

#### Equation for percent by mass:
\[
\% \text{w/w} = \frac{\text{mass of component}}{\text{total mass of alloy}} \times 100\%
\]

#### Percent by mass of copper:
\[
\% \text{w/w (copper)} = \frac{70 \, \text{g}}{100 \, \text{g}} \times 100\% = 70\%
\]

#### Percent by mass of zinc:
\[
\% \text{w/w (zinc)} = \frac{30 \, \text{g}}{100 \, \text{g}} \times 100\% = 30\%
\]

#### Answer:
\[
\boxed{70\% \text{ copper, } 30\% \text{ zinc}}
\]

---

Final Answers:

1. \(\boxed{13.75\%}\)
2. \(\boxed{34.78\%}\)
3. \(\boxed{22.5 \, \text{g}}\)
4. \(\boxed{70\% \text{ copper, } 30\% \text{ zinc}}\)