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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 acetone, dimethyl sulfoxide, carbon tetrachloride, glycerol, 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:

[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Liquid} & \text{Density} \\
\hline
\text{Acetone} & 0.79 \, \text{g/cm}^3 \\
\hline
\text{Dimethyl sulfoxide} & 1.1 \, \text{g/cm}^3 \\
\hline
\text{Carbon tetrachloride} & 1.6 \, \text{g/cm}^3 \\
\hline
\text{Glycerol} & 1.3 \, \text{g/cm}^3 \\
\hline
\text{Methyl acetate} & 0.93 \, \text{g/cm}^3 \\
\hline
\end{tabular}
\][/tex]

Next, the chemist measures the volume of the unknown liquid as 0.597 L and the mass of the unknown liquid as 472 g.

[tex]\[
\begin{tabular}{|c|c|}
\hline
\begin{tabular}{l}
Calculate the density of the liquid. Round \\
your answer to 3 significant digits.
\end{tabular} & \boxed{\text{ } \, \text{g/cm}^3} \\
\hline
\begin{tabular}{l}
Given the data above, is it possible to \\
identify the liquid?
\end{tabular} & \begin{tabular}{l}
yes \\
no
\end{tabular} \\
\hline
If it is possible to identify the liquid, do so. & \begin{tabular}{l}
acetone \\
dimethyl sulfoxide \\
carbon tetrachloride \\
glycerol \\
methyl acetate
\end{tabular} \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Sure, let's go through the steps to solve this problem.

### Step 1: Calculating the Density

We are given:
- Mass of the unknown liquid = 472 grams
- Volume of the unknown liquid = 0.597 liters

First, we need to convert the volume from liters to cubic centimeters because the given densities are in grams per cubic centimeter (g/cm³).

1 liter = 1000 cubic centimeters (cm³).

So,
[tex]\[ \text{Volume in cm}^3 = 0.597 \, \text{L} \times 1000 \, \text{cm}^3/\text{L} = 597 \, \text{cm}^3 \][/tex]

Next, we calculate the density:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
[tex]\[ \text{Density} = \frac{472 \, \text{g}}{597 \, \text{cm}^3} \][/tex]

[tex]\[ \text{Density} \approx 0.7906197654941374 \, \text{g/cm}^3 \][/tex]

Now, we round this to three significant digits:
[tex]\[ \text{Density} \approx 0.791 \, \text{g/cm}^3 \][/tex]

### Step 2: Comparing with Known Densities

The known densities from the MSDS information are:
- Acetone: [tex]\( 0.79 \, \text{g/cm}^3 \)[/tex]
- Dimethyl sulfoxide: [tex]\( 1.1 \, \text{g/cm}^3 \)[/tex]
- Carbon tetrachloride: [tex]\( 1.6 \, \text{g/cm}^3 \)[/tex]
- Glycerol: [tex]\( 1.3 \, \text{g/cm}^3 \)[/tex]
- Methyl acetate: [tex]\( 0.93 \, \text{g/cm}^3 \)[/tex]

We compare the calculated density (0.791 g/cm³) to the given densities:

- 0.791 is closest to 0.79 (the density of acetone).

### Step 3: Answer the Questions

1. Calculate the density of the liquid. Round your answer to 3 significant digits.
[tex]\[ \boxed{0.791 \, \text{g/cm}^3} \][/tex]

2. Given the data above, is it possible to identify the liquid?
[tex]\[ \boxed{\text{No}} \][/tex]

3. If it is possible to identify the liquid, do so.

In this case, even though the calculated density is very close to the density of acetone, it does not match any of the densities exactly, therefore it is not definitively possible to identify the liquid based on the given densities.

Therefore, the results suggest that:
- It is not possible to definitively identify the liquid based on the data provided. So, we leave this part unmarked (None).

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