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Calculating Mass Density

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, carbon tetrachloride, ethanolamine, dimethyl sulfoxide, and chloroform.

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}{|c|c|}
\hline
Liquid & Density \\
\hline
Diethylamine & [tex]$0.71 \frac{g}{mL}$[/tex] \\
\hline
Carbon tetrachloride & [tex]$1.6 \frac{g}{mL}$[/tex] \\
\hline
Ethanolamine & [tex]$1.0 \frac{g}{mL}$[/tex] \\
\hline
Dimethyl sulfoxide & [tex]$1.1 \frac{g}{mL}$[/tex] \\
\hline
Chloroform & [tex]$1.5 \frac{g}{mL}$[/tex] \\
\hline
\end{tabular}

Next, the chemist measures the volume of the unknown liquid as [tex]$1008 \, cm^3$[/tex] and the mass of the unknown liquid as 1.50 kg.

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{l}
Calculate the density of the liquid. Round \\
your answer to 3 significant digits.
\end{tabular} & [tex]$\square \, g/mL$[/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}
Diethylamine \\
Carbon tetrachloride \\
Ethanolamine \\
Dimethyl sulfoxide \\
Chloroform
\end{tabular} \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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.