To identify the unknown liquid, we need to calculate its density and compare it with the known densities of the liquids listed in the Material Safety Data Sheets (MSDS).
Here are the steps to solve this problem:
1. Convert the mass to grams:
The mass of the unknown liquid is given as [tex]\(1.56 \, \text{kg}\)[/tex]. Since density is typically expressed in [tex]\(\frac{\text{g}}{\text{mL}}\)[/tex] or [tex]\(\frac{\text{g}}{\text{cm}^3}\)[/tex], we need to convert kilograms to grams.
[tex]\(1 \, \text{kg} = 1000 \, \text{g}\)[/tex]
Therefore, the mass in grams is:
[tex]\[
1.56 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 1560 \, \text{g}
\][/tex]
2. Calculate the density of the unknown liquid:
Density is given by the formula:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
The mass of the unknown liquid is [tex]\(1560 \, \text{g}\)[/tex] and the volume is [tex]\(1420 \, \text{cm}^3\)[/tex]. Substituting these values into the formula gives:
[tex]\[
\text{Density} = \frac{1560 \, \text{g}}{1420 \, \text{cm}^3} = 1.0985915492957747 \, \frac{\text{g}}{\text{cm}^3}
\][/tex]
3. Compare the calculated density with the known densities:
The known densities from the MSDS are:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Liquid} & \text{Density} \, (\frac{\text{g}}{\text{cm}^3}) \\
\hline
\text{tetrahydrofuran} & 0.89 \\
\hline
\text{dimethyl sulfoxide} & 1.1 \\
\hline
\text{diethylamine} & 0.71 \\
\hline
\text{methyl acetate} & 0.93 \\
\hline
\text{pentane} & 0.63 \\
\hline
\end{array}
\][/tex]
We observe that the calculated density ([tex]\(1.0985915492957747 \, \frac{\text{g}}{\text{cm}^3}\)[/tex]) is closest to the density of dimethyl sulfoxide ([tex]\(1.1 \, \frac{\text{g}}{\text{cm}^3}\)[/tex]).
Therefore, the unknown liquid in the lab cabinet is most likely dimethyl sulfoxide.
