Answer :
To solve this problem, we need to evaluate the densities of various mixtures made from methanol and 1,2-dichloroethane and observe the behavior of a cube with a known density in these mixtures.
Here’s a step-by-step guide:
1. Understanding the cube's density:
- The cube has a density of 0.92 g/mL.
2. Components of the mixture:
- There are two substances involved:
- Methanol: Density is 0.79 g/mL.
- 1,2-Dichloroethane: Density is 1.25 g/mL.
3. Calculating the volume of each mixture:
- The volume of methanol is constant at 2.00 mL for each mixture.
- The volume of 1,2-dichloroethane varies: 1.00 mL, 2.00 mL, 3.00 mL, 4.00 mL, 5.00 mL, and 6.00 mL.
4. Calculating the total volume of each mixture:
- Total volume = Volume of methanol + Volume of 1,2-dichloroethane
5. Calculating the density of each mixture:
- We use a weighted average formula for density:
[tex]\[
\text{Density of mixture} = \frac{(\text{Volume of methanol} \times \text{Density of methanol}) + (\text{Volume of 1,2-Dichloroethane} \times \text{Density of 1,2-Dichloroethane})}{\text{Total volume of the mixture}}
\][/tex]
6. Evaluating the cube's behavior:
- Compare the density of the cube (0.92 g/mL) with the density of the mixture:
- If the density of the mixture is less than 0.92 g/mL, the cube floats.
- If the density of the mixture is greater than or equal to 0.92 g/mL, the cube is suspended.
Let's summarize the densities and behaviors you would observe based on these calculations:
- For Mixture 1 (Methanol: 2.00 mL, 1,2-Dichloroethane: 1.00 mL), the cube is suspended because the density is 0.943 g/mL.
- For Mixture 2 (Methanol: 2.00 mL, 1,2-Dichloroethane: 2.00 mL), the cube is suspended because the density is 1.02 g/mL.
- For Mixture 3 (Methanol: 2.00 mL, 1,2-Dichloroethane: 3.00 mL), the cube is suspended because the density is 1.066 g/mL.
- For Mixture 4 (Methanol: 2.00 mL, 1,2-Dichloroethane: 4.00 mL), the cube is suspended because the density is 1.097 g/mL.
- For Mixture 5 (Methanol: 2.00 mL, 1,2-Dichloroethane: 5.00 mL), the cube is suspended because the density is 1.119 g/mL.
- For Mixture 6 (Methanol: 2.00 mL, 1,2-Dichloroethane: 6.00 mL), the cube is suspended because the density is 1.135 g/mL.
These steps help ensure that the densities and behaviors of the mixtures are analyzed correctly, demonstrating why the cube behaves as it does in each mixture.
Here’s a step-by-step guide:
1. Understanding the cube's density:
- The cube has a density of 0.92 g/mL.
2. Components of the mixture:
- There are two substances involved:
- Methanol: Density is 0.79 g/mL.
- 1,2-Dichloroethane: Density is 1.25 g/mL.
3. Calculating the volume of each mixture:
- The volume of methanol is constant at 2.00 mL for each mixture.
- The volume of 1,2-dichloroethane varies: 1.00 mL, 2.00 mL, 3.00 mL, 4.00 mL, 5.00 mL, and 6.00 mL.
4. Calculating the total volume of each mixture:
- Total volume = Volume of methanol + Volume of 1,2-dichloroethane
5. Calculating the density of each mixture:
- We use a weighted average formula for density:
[tex]\[
\text{Density of mixture} = \frac{(\text{Volume of methanol} \times \text{Density of methanol}) + (\text{Volume of 1,2-Dichloroethane} \times \text{Density of 1,2-Dichloroethane})}{\text{Total volume of the mixture}}
\][/tex]
6. Evaluating the cube's behavior:
- Compare the density of the cube (0.92 g/mL) with the density of the mixture:
- If the density of the mixture is less than 0.92 g/mL, the cube floats.
- If the density of the mixture is greater than or equal to 0.92 g/mL, the cube is suspended.
Let's summarize the densities and behaviors you would observe based on these calculations:
- For Mixture 1 (Methanol: 2.00 mL, 1,2-Dichloroethane: 1.00 mL), the cube is suspended because the density is 0.943 g/mL.
- For Mixture 2 (Methanol: 2.00 mL, 1,2-Dichloroethane: 2.00 mL), the cube is suspended because the density is 1.02 g/mL.
- For Mixture 3 (Methanol: 2.00 mL, 1,2-Dichloroethane: 3.00 mL), the cube is suspended because the density is 1.066 g/mL.
- For Mixture 4 (Methanol: 2.00 mL, 1,2-Dichloroethane: 4.00 mL), the cube is suspended because the density is 1.097 g/mL.
- For Mixture 5 (Methanol: 2.00 mL, 1,2-Dichloroethane: 5.00 mL), the cube is suspended because the density is 1.119 g/mL.
- For Mixture 6 (Methanol: 2.00 mL, 1,2-Dichloroethane: 6.00 mL), the cube is suspended because the density is 1.135 g/mL.
These steps help ensure that the densities and behaviors of the mixtures are analyzed correctly, demonstrating why the cube behaves as it does in each mixture.
