Math Problem Statement

A chemist working as a safety inspector finds an unmarked bottle in a lab cabinet. The chemist measures the volume of the unknown liquid as 1702 cm³ and the mass as 1.73 kg. Calculate the density of the liquid and identify it based on the provided list of known densities.

Solution

We are tasked with calculating the density of an unknown liquid and then identifying it based on the provided data. Let's go step by step:

Step 1: Calculate the density of the unknown liquid.

The formula for density dd is:

d=mVd = \frac{m}{V}

Where:

  • mm is the mass of the liquid (1.73 kg),
  • VV is the volume of the liquid (1702 cm³, which equals 1702 mL because 1 cm³ = 1 mL).

Before calculating, let's convert the mass from kilograms to grams: 1.73kg=1.73×1000=1730g1.73 \, \text{kg} = 1.73 \times 1000 = 1730 \, \text{g}

Now we calculate the density: d=1730g1702mL1.016g/mLd = \frac{1730 \, \text{g}}{1702 \, \text{mL}} \approx 1.016 \, \text{g/mL}

Step 2: Identify the liquid.

Using the calculated density (1.016 g/mL), let's compare it with the known densities provided:

  • Chloroform: 1.5g/mL1.5 \, \text{g/mL}
  • Pentane: 0.63g/mL0.63 \, \text{g/mL}
  • Carbon tetrachloride: 1.6g/mL1.6 \, \text{g/mL}
  • Diethylamine: 0.71g/mL0.71 \, \text{g/mL}
  • Ethanolamine: 1.0g/mL1.0 \, \text{g/mL}

The calculated density of 1.016 g/mL is closest to ethanolamine (1.0 g/mL).

Step 3: Answer the questions

  • Density of the liquid: 1.016 g/mL
  • Is it possible to identify the liquid? Yes
  • Identified liquid: Ethanolamine

Would you like further clarification or details on this?

Here are 5 related questions to explore:

  1. What factors could influence the accuracy of the density measurement?
  2. How would the density change if the liquid was at a different temperature?
  3. Why is density important in identifying substances?
  4. Can the shape of the container affect the measured volume for irregular liquids?
  5. What is the difference between mass and weight in scientific terms?

Tip: Always ensure temperature and pressure conditions are controlled when measuring physical properties like density, as they can affect the results.

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Math Problem Analysis

Mathematical Concepts

Density
Volume and Mass Conversion
Unit Conversion

Formulas

d = m / V (density = mass / volume)

Theorems

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Suitable Grade Level

Grades 9-12