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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 pentane, dimethyl sulfoxide, carbon tetrachloride, glycerol, and tetrahydrofuran.

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

\begin{tabular}{|r|c|}
\hline
Liquid & Density \\
\hline
Pentane & [tex]$0.63 \, \text{g/cm}^3$[/tex] \\
\hline
Dimethyl sulfoxide & [tex]$1.1 \, \text{g/cm}^3$[/tex] \\
\hline
Carbon tetrachloride & [tex]$1.6 \, \text{g/cm}^3$[/tex] \\
\hline
Glycerol & [tex]$1.3 \, \text{g/cm}^3$[/tex] \\
\hline
Tetrahydrofuran & [tex]$0.89 \, \text{g/cm}^3$[/tex] \\
\hline
\end{tabular}

Next, the chemist measures the volume of the unknown liquid as [tex]$0.630 \, \text{L}$[/tex] and the mass of the unknown liquid as [tex]$694 \, \text{g}$[/tex].

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{l}
Calculate the density of the liquid. Round \\
your answer to 3 significant digits.
\end{tabular} & [tex]$\quad \text{g/cm}^3$[/tex] \\
\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}
pentane \\
dimethyl sulfoxide \\
carbon tetrachloride \\
glycerol \\
tetrahydrofuran
\end{tabular} \\
\hline
\end{tabular}



Answer :

GinnyAnswer
### Step-by-Step Solution:

#### Step 1: Convert Volume to Cubic Centimeters
The volume of the liquid is given in liters (0.630 L). To calculate density, we need the volume in cubic centimeters (cm³) because the densities of the known liquids are provided in grams per cubic centimeter (g/cm³).

1 liter (L) is equivalent to 1000 cubic centimeters (cm³).

[tex]\[ 0.630 \, \text{L} \times 1000 \, \text{cm}^3/\text{L} = 630.0 \, \text{cm}^3 \][/tex]

So, the volume of the liquid is 630.0 cm³.

#### Step 2: Calculate the Density of the Liquid

Density is calculated using the formula:

[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]

Given:
- Mass = 694 grams (g)
- Volume = 630.0 cm³

[tex]\[ \text{Density} = \frac{694 \, \text{g}}{630.0 \, \text{cm}^3} \approx 1.102 \, \text{g/cm}^3 \][/tex]

Rounding to 3 significant digits, the density of the liquid is:

[tex]\[ \text{Density} \approx 1.102 \, \text{g/cm}^3 \][/tex]

#### Step 3: Compare the Calculated Density with Known Densities

Now we compare the calculated density (1.102 g/cm³) to the known densities from the chemist's collection of Material Safety Data Sheets (MSDS):

- Pentane: [tex]\(0.63 \, \text{g/cm}^3\)[/tex]
- Dimethyl sulfoxide: [tex]\(1.1 \, \text{g/cm}^3\)[/tex]
- Carbon tetrachloride: [tex]\(1.6 \, \text{g/cm}^3\)[/tex]
- Stycerol: [tex]\(1.3 \, \text{g/cm}^3\)[/tex]
- Tetrahydrofuran: [tex]\(0.89 \, \text{g/cm}^3\)[/tex]

#### Step 4: Identify the Liquid

The calculated density (1.102 g/cm³) is very close to the density of dimethyl sulfoxide (1.1 g/cm³), but it's not exact when rounded to 3 significant digits. None of the known liquid densities exactly match 1.102 g/cm³ when rounded to three significant digits.

#### Conclusion

- Calculated Density: [tex]\(1.102 \, \text{g/cm}^3\)[/tex]
- Is it possible to identify the liquid?: No, because the calculated density does not match exactly with any of the provided known densities.
- Identified Liquid: None.

Therefore, based on the given data, it is not possible to definitely identify the liquid from the provided options.

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