Question

(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a 45 -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 isopropylalcohol (density 0.785 \(\mathrm{g} / \mathrm{mL}\) )or toluene (density 0.866 \(\mathrm{g} / \mathrm{mL} ) .\) 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 cylin-der. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the accuracy of measurement needed? (d) 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

(a) The calculated density of the liquid substance is 0.8555 g/mL, and its probable identity is toluene. (b) To obtain 45.0 g of ethylene glycol, 40.4 mL of the liquid should be used. (c) A graduated cylinder may not provide the desired accuracy of measurement in some cases due to human error and inaccurate markings. (d) The mass of a nickel cube with 5 cm edge length is 1112.50 g.

Step-by-step solution

(a) Calculate the density of the liquid substance

To calculate the density of the substance, we will use the formula: \(Density = \frac{Mass}{Volume}\). In this case, mass = 38.5 g, and volume = 45 mL. Density = \(\frac{38.5\mathrm{g}}{45\mathrm{mL}}\) = 0.8555 g/mL.

(a) Determine the probable identity of the substance

We now need to identify if the substance is isopropyl alcohol (density 0.785 g/mL) or toluene (density 0.866 g/mL). Since the calculated density (0.8555 g/mL) is closer to the density of toluene, we can conclude that the substance is likely to be toluene.

(b) Calculate the volume of ethylene glycol required

In this part, we are given the mass of ethylene glycol (45 g) and its density (1.114 g/mL). We need to find the volume of the ethylene glycol. Using the formula for density, we can rearrange it to find the volume: \(Volume = \frac{Mass}{Density}\). Volume = \(\frac{45.0\mathrm{g}}{1.114\mathrm{g/mL}}\) = 40.4 mL.

(c) Comment on the accuracy of using a graduated cylinder

A graduated cylinder is likely to be less accurate than using a balance since it only measures volume rather than mass. Human error and inaccurate markings on the graduated cylinder can lead to small discrepancies in the measured volume. Therefore, it may not afford the desired accuracy of measurement in some cases.

(d) Calculate the mass of the nickel cube

In this part, we have a nickel cube with a side of 5 cm and a density of 8.90 g/cm³. To find the mass of the cube, we need to find its volume first: \(Volume = Side^3\). Volume = \((5.00\mathrm{cm})^3\) = 125 cm³. Now using the density of nickel (8.90 g/cm³), we can find the mass as: Mass = Density × Volume. Mass = \(8.90\mathrm{g/cm^3} \times 125\mathrm{cm^3}\) = 1112.50 g. So, the mass of the nickel cube is 1112.50 g.

Key concepts

Density Formula

Density is a fundamental concept in chemistry which helps us compare how much mass is packed into a given volume. The formula for calculating density is quite straightforward: **Density = Mass / Volume**.

To put it simply, density tells us how tightly matter is crammed together in a substance. In the example given, a student measures a liquid's mass (38.5 grams) and its volume (45 milliliters) to calculate its density. Using the formula, she finds that the density is 0.8555 g/mL.

This simple calculation is essential for identifying substances, as different materials often have different densities. By knowing a substance's density, one can compare it to reference values to determine its likely identity. This is a compelling application of the density formula in practical scenarios.

Volume Measurement

Volume measurement is crucial in experiments involving liquids. In the exercise provided, a graduated cylinder was used to measure the volume of both the liquid sample and ethylene glycol. The measured volume of the liquid was essential to determine its density.

Graduated cylinders are common laboratory tools that provide a quick way to measure a fluid's volume. They work by marking the cylinder at various heights to indicate how much liquid is present.

• Despite their convenience, there are a few concerns about accuracy.
• Inaccuracies can occur due to imperfect markings or human errors in reading the level of contents.

For precise experiments, choosing the right tool and properly reading measurements are key to obtaining accurate data.

Chemical Identification

Identifying a chemical substance using its density is an intriguing process. Once the density is calculated, it can be compared to known densities of possible substances. In the exercise, this method was used to decide which chemical substance the student was testing.

For example, after calculating the density of a liquid sample as 0.8555 g/mL, the student compared this result to densities of known substances: isopropyl alcohol at 0.785 g/mL and toluene at 0.866 g/mL. Since the calculated density was closer to that of toluene, the student concluded that the unknown substance was likely toluene.

This is a classic example of how chemical identification using density can help in narrowing down possibilities and confirming the nature of a sample based on empirical data.

Mass Calculation

Mass calculation is another principal element in understanding material properties. In the exercise, the mass of different substances was a key factor in calculations.

To find mass when you have volume and density, you use the rearranged formula: Mass = Density × Volume.

For instance, knowing the nickel cube's density (8.90 g/cm³) and its side length (5.00 cm), the volume (125 cm³) was already determined through the calculation of its cube dimensions. Multiplying this volume by the density gives the mass of the cube, which is 1112.50 grams.

This method shows that, given an object’s shape, size, and density, one can determine its mass. Such exercises enhance the understanding of properties while reinforcing straightforward, yet vital, calculations in science.