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Sagot :
To solve this problem, we need to calculate the density of the unknown liquid and then compare it to the known densities of the given liquids.
### Step 1: Convert Mass to Consistent Units
First, we start by converting the mass of the liquid from kilograms to grams. This is necessary because the densities given are in grams per milliliter (g/mL), and we need the mass in grams to ensure unit consistency in our calculations.
The given mass is:
[tex]\[ 1.79 \, \text{kg} \][/tex]
To convert this to grams:
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
[tex]\[ 1.79 \, \text{kg} \times 1000 \, \text{g/kg} = 1790 \, \text{g} \][/tex]
### Step 2: Calculate the Density
The density [tex]\( \rho \)[/tex] of a substance is given by the formula:
[tex]\[ \rho = \frac{\text{mass}}{\text{volume}} \][/tex]
We know the mass of the liquid is:
[tex]\[ 1790 \, \text{g} \][/tex]
and the volume is:
[tex]\[ 1911 \, \text{cm}^3 \][/tex]
Note: Since [tex]\(1 \, \text{cm}^3 = 1 \, \text{mL}\)[/tex], the volume in milliliters ([tex]\(mL\)[/tex]) is also [tex]\(1911 \, \text{mL}\)[/tex].
Now, we can calculate the density:
[tex]\[ \rho = \frac{1790 \, \text{g}}{1911 \, \text{mL}} \][/tex]
[tex]\[ \rho \approx 0.937 \, \text{g/mL} \][/tex]
### Step 3: Compare to Known Densities
Next, we compare the calculated density to the known densities of the possible liquids provided:
- Diethylamine: [tex]\(0.71 \, \text{g/mL}\)[/tex]
- Acetone: [tex]\(0.79 \, \text{g/mL}\)[/tex]
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/mL}\)[/tex]
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/mL}\)[/tex]
- Methyl acetate: [tex]\(0.93 \, \text{g/mL}\)[/tex]
### Step 4: Determine the Identity
Our calculated density is:
[tex]\[ 0.937 \, \text{g/mL} \][/tex]
When rounding to three significant digits, we get:
[tex]\[ 0.937 \][/tex]
We see that this density does not exactly match any of the given liquids. The closest value is that of methyl acetate ([tex]\(0.93 \, \text{g/mL}\)[/tex]), but they are not identical when rounded to three significant digits.
### Conclusion
Given the calculated density of [tex]\(0.937 \, \text{g/mL}\)[/tex] and the list of known densities, it is not possible to identify the liquid precisely from the provided data, as there is no exact match.
Thus, the liquid remains unidentified based on the density alone.
### Step 1: Convert Mass to Consistent Units
First, we start by converting the mass of the liquid from kilograms to grams. This is necessary because the densities given are in grams per milliliter (g/mL), and we need the mass in grams to ensure unit consistency in our calculations.
The given mass is:
[tex]\[ 1.79 \, \text{kg} \][/tex]
To convert this to grams:
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
[tex]\[ 1.79 \, \text{kg} \times 1000 \, \text{g/kg} = 1790 \, \text{g} \][/tex]
### Step 2: Calculate the Density
The density [tex]\( \rho \)[/tex] of a substance is given by the formula:
[tex]\[ \rho = \frac{\text{mass}}{\text{volume}} \][/tex]
We know the mass of the liquid is:
[tex]\[ 1790 \, \text{g} \][/tex]
and the volume is:
[tex]\[ 1911 \, \text{cm}^3 \][/tex]
Note: Since [tex]\(1 \, \text{cm}^3 = 1 \, \text{mL}\)[/tex], the volume in milliliters ([tex]\(mL\)[/tex]) is also [tex]\(1911 \, \text{mL}\)[/tex].
Now, we can calculate the density:
[tex]\[ \rho = \frac{1790 \, \text{g}}{1911 \, \text{mL}} \][/tex]
[tex]\[ \rho \approx 0.937 \, \text{g/mL} \][/tex]
### Step 3: Compare to Known Densities
Next, we compare the calculated density to the known densities of the possible liquids provided:
- Diethylamine: [tex]\(0.71 \, \text{g/mL}\)[/tex]
- Acetone: [tex]\(0.79 \, \text{g/mL}\)[/tex]
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/mL}\)[/tex]
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/mL}\)[/tex]
- Methyl acetate: [tex]\(0.93 \, \text{g/mL}\)[/tex]
### Step 4: Determine the Identity
Our calculated density is:
[tex]\[ 0.937 \, \text{g/mL} \][/tex]
When rounding to three significant digits, we get:
[tex]\[ 0.937 \][/tex]
We see that this density does not exactly match any of the given liquids. The closest value is that of methyl acetate ([tex]\(0.93 \, \text{g/mL}\)[/tex]), but they are not identical when rounded to three significant digits.
### Conclusion
Given the calculated density of [tex]\(0.937 \, \text{g/mL}\)[/tex] and the list of known densities, it is not possible to identify the liquid precisely from the provided data, as there is no exact match.
Thus, the liquid remains unidentified based on the density alone.
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