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A chemist working as a safety inspector finds an unmarked bottle in a lab cabinet. A note on the door of the cabinet says the cabinet is used to store bottles of diethylamine, acetone, dimethyl sulfoxide, carbon tetrachloride, and methyl acetate.

The chemist plans to try to identify the unknown liquid by measuring the density and comparing it to known densities. First, from his collection of Material Safety Data Sheets (MSDS), the chemist finds the following information:

\begin{tabular}{|c|c|}
\hline
Liquid & Density \\
\hline
diethylamine & [tex]$0.71 \, \text{g/mL}$[/tex] \\
\hline
acetone & [tex]$0.79 \, \text{g/mL}$[/tex] \\
\hline
dimethyl sulfoxide & [tex]$1.1 \, \text{g/mL}$[/tex] \\
\hline
carbon tetrachloride & [tex]$1.6 \, \text{g/mL}$[/tex] \\
\hline
methyl acetate & [tex]$0.93 \, \text{g/mL}$[/tex] \\
\hline
\end{tabular}

Next, the chemist measures the volume of the unknown liquid as [tex]$1911 \, \text{cm}^3$[/tex] and the mass of the unknown liquid as [tex]$1.79 \, \text{kg}$[/tex].

Calculate the density of the liquid. Round your answer to 3 significant digits.

[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{1.79 \, \text{kg}}{1911 \, \text{cm}^3}
\][/tex]

Given the data above, is it possible to identify the liquid? If so, do so.

A. diethylamine
B. acetone
C. dimethyl sulfoxide
D. carbon tetrachloride
E. methyl acetate



Answer :

GinnyAnswer
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.

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