Science worksheet on solution concentration and density, featuring two problems with beakers labeled A-D.

Problem Analysis and Solution

The problem involves understanding the concepts of concentration and density in solutions. Let's break it down step by step.

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#### Part 1: Which solutions have the same concentration and density?

Concentration is defined as the amount of solute (sugar) per unit volume of solution. It can be expressed as:

\[
\text{Concentration} = \frac{\text{Mass of Solute}}{\text{Volume of Solution}}
\]

We need to calculate the concentration for each beaker and compare them.

##### Calculations for Beakers A, B, C, and D:

1. Beaker A:
- Mass of sugar = 4 g
- Volume of solution = 25 mL
- Concentration = \(\frac{4 \, \text{g}}{25 \, \text{mL}} = 0.16 \, \text{g/mL}\)

2. Beaker B:
- Mass of sugar = 4 g
- Volume of solution = 50 mL
- Concentration = \(\frac{4 \, \text{g}}{50 \, \text{mL}} = 0.08 \, \text{g/mL}\)

3. Beaker C:
- Mass of sugar = 2 g
- Volume of solution = 25 mL
- Concentration = \(\frac{2 \, \text{g}}{25 \, \text{mL}} = 0.08 \, \text{g/mL}\)

4. Beaker D:
- Mass of sugar = 8 g
- Volume of solution = 50 mL
- Concentration = \(\frac{8 \, \text{g}}{50 \, \text{mL}} = 0.16 \, \text{g/mL}\)

##### Comparison:
- Beaker A: \(0.16 \, \text{g/mL}\)
- Beaker B: \(0.08 \, \text{g/mL}\)
- Beaker C: \(0.08 \, \text{g/mL}\)
- Beaker D: \(0.16 \, \text{g/mL}\)

From the calculations, we see that:
- Beakers A and D have the same concentration (\(0.16 \, \text{g/mL}\)).
- Beakers B and C have the same concentration (\(0.08 \, \text{g/mL}\)).

Since the density of a solution is directly related to its concentration (assuming the solute and solvent have similar densities), the solutions with the same concentration will also have the same density.

Answer for Part 1:
\[
\boxed{\text{A and D, B and C}}
\]

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#### Part 2: How many grams of sugar should beaker B contain to have the same density as beaker A?

To have the same density as beaker A, beaker B must have the same concentration as beaker A. The concentration of beaker A is \(0.16 \, \text{g/mL}\).

The volume of beaker B is 25 mL. To find the required mass of sugar, we use the concentration formula:

\[
\text{Concentration} = \frac{\text{Mass of Solute}}{\text{Volume of Solution}}
\]

Rearranging for the mass of solute:

\[
\text{Mass of Solute} = \text{Concentration} \times \text{Volume of Solution}
\]

Substitute the values:
\[
\text{Mass of Solute} = 0.16 \, \text{g/mL} \times 25 \, \text{mL} = 4 \, \text{g}
\]

Answer for Part 2:
\[
\boxed{4}
\]

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#### Part 3: How many grams of sugar should beaker D contain to have the same density as beaker C?

To have the same density as beaker C, beaker D must have the same concentration as beaker C. The concentration of beaker C is \(0.08 \, \text{g/mL}\).

The volume of beaker D is 100 mL. To find the required mass of sugar, we use the concentration formula:

\[
\text{Concentration} = \frac{\text{Mass of Solute}}{\text{Volume of Solution}}
\]

Rearranging for the mass of solute:

\[
\text{Mass of Solute} = \text{Concentration} \times \text{Volume of Solution}
\]

Substitute the values:
\[
\text{Mass of Solute} = 0.08 \, \text{g/mL} \times 100 \, \text{mL} = 8 \, \text{g}
\]

Answer for Part 3:
\[
\boxed{8}
\]

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Final Answers:

1. \(\boxed{\text{A and D, B and C}}\)
2. \(\boxed{4}\)
3. \(\boxed{8}\)