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(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) Is a graduated cylinder such as that shown in Figure \(1.19\) 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?

Step by step solution

01

Calculate the density of the substance

Using the given data, the sample's mass is 38.5 g, and the volume is 45 mL. To find the density, use the formula: \(density = \frac{mass}{volume}\) Plug in the given values: \(density = \frac{38.5}{45}\) Calculate the density: \(density ≈ 0.855 \mathrm{~g} / \mathrm{mL}\)

02

Determine the probable identity

Compare the calculated density with the given densities of isopropyl alcohol and toluene: Isopropyl alcohol has a density of \(0.785 \mathrm{~g} / \mathrm{mL}\) Toluene has a density of \(0.866 \mathrm{~g} / \mathrm{mL}\) Since the calculated density (0.855 g/mL) is closer to the density of toluene, it is reasonable to assume that the substance is toluene. b) Finding the volume of ethylene glycol to obtain a 45.0 g sample

03

Use the density formula

To find the required volume, use the formula: \(volume = \frac{mass}{density}\) The density of ethylene glycol is given as \(1.114 \mathrm{~g} / \mathrm{mL}\) and the required mass is 45.0 g.

04

Calculate the volume

Plug in the given values into the equation: \(volume = \frac{45.0}{1.114}\) Calculate the volume: \(volume ≈ 40.4 \mathrm{~mL}\) c) Assessing the accuracy of the graduated cylinder A typical graduated cylinder's accuracy depends on its size but is usually around ±1%. The chemist can indeed use the graduated cylinder to achieve the desired mass with reasonable accuracy, considering its acceptable tolerance for this measurement. d) Calculating the mass of a nickel cube

05

Calculate the volume of the cube

The cube has an edge length of 5.00 cm. The volume of a cube can be calculated using the formula: \(Volume = (Edge Length)^3\) Plug in the given values: \(Volume = (5.00)^3 = 125.0 \mathrm{~cm}^{3}\)

06

Use the density formula to find the mass

The density formula can now be used to find the mass: \(mass = density × volume\) The density of nickel is given as \(8.90 \mathrm{~g} / \mathrm{cm}^{3}\). Plug in the given values into the equation: \(mass = 8.90 × 125.0\) Calculate the mass: \(mass = 1112.5 \mathrm{~g}\) The mass of the cubic piece of nickel is 1112.5 g.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Density Calculation

Understanding density is crucial when dealing with various substances in science. Density calculation combines the mass and volume of an object and is expressed with the formula \(density = \frac{mass}{volume}\). To put it simply, if you have a sample weighing 38.5 grams and occupying a space of 45 mL, like in our exercise, the density can be found by dividing the mass by the volume.

To determine the density of the substance in question, the formula gives us \(density = \frac{38.5g}{45mL} \) which approximates to \(0.855 g/mL\). This calculated density can be compared with known densities of various substances to identify the unknown substance, showing the practical application of density in real-world situations.

Volume Calculation

Volume calculation is a common task in the laboratory when working with liquids, and it's vital for experiments where precise measurements are necessary. The formula for calculating the volume of a liquid from its mass and density is \(volume = \frac{mass}{density}\). For instance, if a chemist needs 45.0 grams of ethylene glycol, and its density is known to be \(1.114 g/mL\), the volume of liquid required is computed as \(\frac{45.0g}{1.114g/mL} \) which gives us approximately \(40.4 mL\).

Knowing how to calculate volume correctly ensures the accuracy of component amounts in a mixture or solution, crucial for the consistency and success of laboratory work.

Graduated Cylinder Usage

Accurate measurements of liquids in a laboratory setting are often carried out using a graduated cylinder. To ensure precision when using a graduated cylinder, it is essential to understand its proper usage. Graduated cylinders come in various sizes, and selecting the appropriate size for the volume being measured can significantly increase accuracy.

The accuracy of a typical graduated cylinder is usually within ±1% of the total volume. For instance, when measuring out a specific volume of a liquid like ethylene glycol, the chemist can achieve the required 40.4 mL with reasonable accuracy, provided they read the meniscus at eye level and handle the cylinder correctly. Efficient use of this simple yet significant piece of lab equipment is essential for measurement reliability.

Substance Identification

Substance identification via density measurement is a prime example of density's application in a real-world scenario. By comparing an unknown substance's measured density to that of known substances, one can identify the unknown. In our textbook case, after calculating the density of the liquid to be approximately \(0.855 g/mL\) and comparing it with the known densities of isopropyl alcohol (\(0.785 g/mL\) ) and toluene (\(0.866 g/mL\) ), we can infer the substance is likely toluene, because its density value is closest to the obtained density.

The fundamental concept of measuring and comparing densities is a tool widely used across various fields, such as material science, chemistry, and environmental studies, to name among many applications.