(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 \(0.866 \mathrm{~g} / \mathrm{mL}\) ). 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 cylinder. 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 (d) A cubic piece of metal accuracy of measurement needed? 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

We need to calculate the density of the given substance by dividing its mass by its volume. The formula for density is: Density \(= \frac{Mass}{Volume}\) Mass \(= 38.5 \mathrm{~g}\) Volume \(= 45 \mathrm{~mL}\) Density \(= \frac{38.5 \mathrm{~g}}{45 \mathrm{~mL}}\)

02

Compare the calculated density to given densities

After calculating the density of the given substance, we will compare it to the densities of isopropyl alcohol and toluene to identify the substance. Isopropyl alcohol density \(= 0.785 \mathrm{~g/ mL}\) Toluene density \(= 0.866 \mathrm{~g/ mL}\) (b) Calculating the Volume of Ethylene Glycol

03

Use the given mass and density of ethylene glycol to calculate the volume

To find the volume of ethylene glycol, we can rearrange the density formula as: Volume \(= \frac{Mass}{Density}\) Mass \(= 45.0 \mathrm{~g}\) Ethylene glycol density \(= 1.114 \mathrm{~g/ mL}\) Volume \(= \frac{45.0 \mathrm{~g}}{1.114 \mathrm{~g/ mL}}\) (c) Graduated Cylinder Accuracy

04

Comment on the likely accuracy of the graduated cylinder for measurement

The accuracy of a graduated cylinder is typically limited by the level of precision it can measure, which depends on the spacing of the graduation marks and the ability to read the meniscus level accurately. A chemist must consider whether the graduated cylinder provides sufficient accuracy for the specific experiment or if other more accurate measuring devices, like volumetric pipettes, should be used instead. (d) Calculating the Mass of the Nickel Cube

05

Calculate the volume of the cube

To find the volume of the cube, we can use the formula: Volume \(= Length × Width × Height\) Since all edges are equal in length: Volume \(= (5.00 \mathrm{~cm})^{3}\)

06

Use the given density and volume to calculate the mass

To find the mass of the nickel cube, we can use the rearranged density formula: Mass \(= Density × Volume\) Density \(= 8.90 \mathrm{~g/cm^{3}}\) Volume \(= (5.00 \mathrm{~cm})^{3}\) Mass \(= 8.90 \mathrm{~g/cm^{3}} × (5.00 \mathrm{~cm})^{3}\)

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