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Sagot :
Let's go through the problem step-by-step to calculate the density of the liquid, check if it is possible to identify the liquid, and if so, identify which liquid it might be.
### Step 1: Convert Mass to Grams
The mass of the unknown liquid is given as [tex]\(1.50 \, \text{kg}\)[/tex]. To work with density in [tex]\(\text{g/cm}^3\)[/tex] or [tex]\(\text{g/mL}\)[/tex], we need to convert the mass to grams.
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
[tex]\[ \text{mass} = 1.50 \, \text{kg} \times 1000 = 1500 \, \text{g} \][/tex]
### Step 2: Calculate the Density
The volume of the unknown liquid is given as [tex]\(1008 \, \text{cm}^3\)[/tex].
Density is calculated using the formula:
[tex]\[ \text{density} = \frac{\text{mass}}{\text{volume}} \][/tex]
Substituting the values for mass and volume:
[tex]\[ \text{density} = \frac{1500 \, \text{g}}{1008 \, \text{cm}^3} \approx 1.488 \, \text{g/cm}^3 \][/tex]
### Step 3: Compare with Known Densities
The known densities from the Material Safety Data Sheets (MSDS) are:
- Diethylamine: [tex]\(0.71 \, \text{g/mL}\)[/tex]
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/mL}\)[/tex]
- Ethanolamine: [tex]\(1.0 \, \text{g/mL}\)[/tex]
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/mL}\)[/tex]
- Chloroform: [tex]\(1.5 \, \text{g/mL}\)[/tex]
### Step 4: Determine if Identification is Possible
The calculated density of the unknown liquid is [tex]\(1.488 \, \text{g/cm}^3\)[/tex] or [tex]\(1.488 \, \text{g/mL}\)[/tex]. Now we will check if this matches any of the known densities.
Rounding the calculated density to three significant digits, we get:
[tex]\[ 1.488 \rightarrow 1.49 \, \text{g/mL} \][/tex]
Comparing rounded density with known densities:
- Diethylamine: [tex]\(0.71 \, \text{g/mL}\)[/tex] (not a match)
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/mL}\)[/tex] (not a match)
- Ethanolamine: [tex]\(1.0 \, \text{g/mL}\)[/tex] (not a match)
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/mL}\)[/tex] (not a match)
- Chloroform: [tex]\(1.5 \, \text{g/mL}\)[/tex] (not a match)
Based on these data, the calculated density of [tex]\(1.488 \, \text{g/mL}\)[/tex] does not match exactly with any of the provided densities.
### Conclusion
- Density of the liquid: [tex]\(1.49 \, \text{g/mL}\)[/tex]
- Is it possible to identify the liquid?: No
Since the calculated density does not match any of the known densities to three significant digits, it is not possible to conclusively identify the liquid based on the provided data.
### Step 1: Convert Mass to Grams
The mass of the unknown liquid is given as [tex]\(1.50 \, \text{kg}\)[/tex]. To work with density in [tex]\(\text{g/cm}^3\)[/tex] or [tex]\(\text{g/mL}\)[/tex], we need to convert the mass to grams.
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
[tex]\[ \text{mass} = 1.50 \, \text{kg} \times 1000 = 1500 \, \text{g} \][/tex]
### Step 2: Calculate the Density
The volume of the unknown liquid is given as [tex]\(1008 \, \text{cm}^3\)[/tex].
Density is calculated using the formula:
[tex]\[ \text{density} = \frac{\text{mass}}{\text{volume}} \][/tex]
Substituting the values for mass and volume:
[tex]\[ \text{density} = \frac{1500 \, \text{g}}{1008 \, \text{cm}^3} \approx 1.488 \, \text{g/cm}^3 \][/tex]
### Step 3: Compare with Known Densities
The known densities from the Material Safety Data Sheets (MSDS) are:
- Diethylamine: [tex]\(0.71 \, \text{g/mL}\)[/tex]
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/mL}\)[/tex]
- Ethanolamine: [tex]\(1.0 \, \text{g/mL}\)[/tex]
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/mL}\)[/tex]
- Chloroform: [tex]\(1.5 \, \text{g/mL}\)[/tex]
### Step 4: Determine if Identification is Possible
The calculated density of the unknown liquid is [tex]\(1.488 \, \text{g/cm}^3\)[/tex] or [tex]\(1.488 \, \text{g/mL}\)[/tex]. Now we will check if this matches any of the known densities.
Rounding the calculated density to three significant digits, we get:
[tex]\[ 1.488 \rightarrow 1.49 \, \text{g/mL} \][/tex]
Comparing rounded density with known densities:
- Diethylamine: [tex]\(0.71 \, \text{g/mL}\)[/tex] (not a match)
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/mL}\)[/tex] (not a match)
- Ethanolamine: [tex]\(1.0 \, \text{g/mL}\)[/tex] (not a match)
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/mL}\)[/tex] (not a match)
- Chloroform: [tex]\(1.5 \, \text{g/mL}\)[/tex] (not a match)
Based on these data, the calculated density of [tex]\(1.488 \, \text{g/mL}\)[/tex] does not match exactly with any of the provided densities.
### Conclusion
- Density of the liquid: [tex]\(1.49 \, \text{g/mL}\)[/tex]
- Is it possible to identify the liquid?: No
Since the calculated density does not match any of the known densities to three significant digits, it is not possible to conclusively identify the liquid based on the provided data.
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