(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?

Step by step solution

01

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. \[density = \frac{38.5}{45} = 0.85556 \mathrm{~g/ml}\]

02

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

03

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

04

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. \[volume = 5.00^{3} = 125 \mathrm{~cm^{3}}\]

05

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 \(1112.5 \mathrm{~g}\).

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