Question

(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\) sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL})\) or toluene (density \(0.866 / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires \(45.0 \mathrm{~g}\) of ethylene glycol, a liquid whose density is \(1.114 \mathrm{~g} / \mathrm{mL}\). Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) A cubic piece of metal measures \(5.00 \mathrm{~cm}\) on each edge. If the metal is nickel, whose density is \(8.90 \mathrm{~g} / \mathrm{cm}^{3},\) what is the mass of the cube?

Short answer

The calculated density of the liquid substance is \(0.85556 \mathrm{~g/ml}\), and it is most likely toluene. To obtain \(45.0 \mathrm{~g}\) of ethylene glycol, the chemist should use approximately \(40.39 \mathrm{~mL}\). The mass of the nickel cube is approximately \(1112.5 \mathrm{~g}\).

Step-by-step solution

Find the density of the substance

To find the density, we can use the formula: \[density = \frac{mass}{volume}\] We are given mass = \(38.5 \mathrm{~g}\) and volume = \(45 \mathrm{~mL}\). Let's plug in these values and find the density of the substance. \[density = \frac{38.5}{45} = 0.85556 \mathrm{~g/ml}\]

Identify the substance

Now we'll compare the calculated density to the given densities of isopropyl alcohol and toluene: Isopropyl alcohol: density = \(0.785 \mathrm{~g/ml}\) Toluene: density = \(0.866 \mathrm{~g/ml}\) Since the calculated density (\(0.85556 \mathrm{~g/ml}\)) is closer to the density of Toluene, the liquid substance is most likely toluene. (b) Calculating the volume of ethylene glycol

Use the density formula to find volume

To find the volume, we can rearrange the density formula to: \[volume = \frac{mass}{density}\] We are given mass = \(45.0 \mathrm{~g}\) and density of ethylene glycol = \(1.114 \mathrm{~g/ml}\). Let's plug in these values and find the volume required. \[volume = \frac{45.0}{1.114} = 40.39 \mathrm{~mL}\] Thus, the chemist should use approximately \(40.39 \mathrm{~mL}\) of ethylene glycol in this experiment. (c) Calculating the mass of a nickel cube

Find the volume of the cube

The formula for the volume of a cube is given by: \[volume = edge^{3}\] Where 'edge' is the length of one edge of the cube. We are given edge = \(5.00 \mathrm{~cm}\). Let's find the volume of the cube. \[volume = 5.00^{3} = 125 \mathrm{~cm^{3}}\]

Calculate the mass of the cube

Now, we'll use the density formula to find the mass of the cube: \[mass = density \times volume\] We are given density of nickel = \(8.90 \mathrm{~g/cm^{3}}\) and volume we just calculated = \(125 \mathrm{~cm^{3}}\). Let's plug in these values and find the mass of the cube. \[mass = 8.90 \times 125 = 1112.5 \mathrm{~g}\] The mass of the nickel cube is approximately \(1112.5 \mathrm{~g}\).

Key concepts

Identification of Substances

When tasked with identifying a liquid from a set of possibilities, determining its density offers a reliable method to narrow down the options. In our exercise, a student had to identify a liquid that could either be isopropyl alcohol or toluene. Density is a characteristic property of substances, meaning that each substance has a unique density under specific conditions. By calculating the liquid's density and comparing it to known densities, we can identify the liquid.
In this scenario, the student measured the mass of the liquid as 38.5 grams and its volume at 45 milliliters. Using the density formula, the student calculated a density of about 0.856 g/mL. This value was closer to the known density of toluene (0.866 g/mL) than to that of isopropyl alcohol (0.785 g/mL), suggesting that the liquid was most likely to be toluene.

To identify substances using density:

• Measure mass and volume precisely.
• Calculate the density using the formula \(density = \frac{mass}{volume}\).
• Compare with known densities to identify the substance.
  
  

Density Formula

The density formula is a simple yet powerful tool in chemical problem solving. It expresses the relationship between mass and volume, allowing us to determine a third value if two are known. Often expressed as \(density = \frac{mass}{volume}\), this formula is central in fields like chemistry and physics.
Density provides crucial information about a substance's compactness. A higher density indicates that the substance has more mass packed into a given volume. Conversely, a lower density means the substance is less tightly packed.

• To find density, divide the mass by the volume.
• Units for density are typically g/mL or g/cm³.
• Interpret the density value to infer about the compactness and type of the substance.
  

Understanding the density formula and its implications can assist in various scientific analyses, including identifying unknown substances and predicting their behaviors in different conditions.

Volume Calculation

Calculating volume is necessary in many scientific experiments, especially when precise measurements of liquids or solids are required. In chemical problem solving, if you know the mass and the density of a substance, you can determine its volume using the rearranged density formula: \(volume = \frac{mass}{density}\).
This formula was particularly useful in determining the volume of ethylene glycol needed, given we knew both its mass (45.0 g) and density (1.114 g/mL). By applying the formula, we found the volume to be approximately 40.39 mL.

Key points for volume calculation include:

• Measure the mass accurately.
• Use the known density or calculate it if necessary.
• Compute the volume using \(volume = \frac{mass}{density}\).
• Ensure consistent units when using the formula.
  

Accurate volume calculations are critical for achieving desired concentrations and reactions in chemical experiments.

Chemical Problem Solving

Chemical problem solving often requires applying several concepts and mathematical formulas simultaneously to draw meaningful conclusions. In our exercise, we integrated concepts of density and volume to solve multiple parts of the problem.
Let's take, for instance, the calculation of the nickel cube’s mass. Knowing the cube’s dimensions (5.00 cm per side), we first calculated its volume using \(volume = edge^3\), resulting in 125 cm³. Next, using the formula \(mass = density \times volume\), and the known density of nickel (8.90 g/cm³), we determined that the mass was approximately 1112.5 grams.
For successful chemical problem solving:

• Understand and identify the data given and what needs to be solved.
• Choose the right formulas (e.g., density, volume) based on the available data.
• Perform calculations accurately, ensuring units are consistent.
• Double-check results against possible known values to ensure they make sense.
  

By mastering these strategies, you can solve complex chemical problems efficiently and accurately.