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Chapter 1: Problem 28

(a) A cube of osmium metal \(1.500 \mathrm{~cm}\) on a side has a mass of \(76.31 \mathrm{~g}\) at \(25^{\circ} \mathrm{C}\). What is its density in \(\mathrm{g} / \mathrm{cm}^{3}\) at this temperature? (b) The density of titanium metal is \(4.51 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\). What mass of titanium displaces \(125.0 \mathrm{~mL}\) of water at \(25^{\circ} \mathrm{C} ?\) (c) The density of benzene at \(15^{\circ} \mathrm{C}\) is \(0.8787 \mathrm{~g} / \mathrm{mL} .\) Calculate the mass of \(0.1500 \mathrm{~L}\) of benzene at this temperature.

Short Answer

Expert verified
(a) The density of the osmium cube at $25^{\circ}\mathrm{C}$ is \(\frac{76.31\,\text{g}}{(1.500\,\text{cm})^3}\) = \(22.59\,\text{g/cm}^3\). (b) The mass of titanium that displaces $125.0\,\text{mL}$ of water at $25^{\circ}\mathrm{C}$ is (4.51 g/cm³) × (125.0 cm³) = \(564\,\text{g}\). (c) The mass of $0.1500\,\text{L}$ of benzene at $15^{\circ}\mathrm{C}$ is (0.8787 g/mL) × (0.1500 × 1000 mL) = \(131.8\,\text{g}\).

Step by step solution

01

Determine the volume of osmium cube

Given, the osmium cube has a side length of 1.500 cm. So we calculate the volume of the cube by using the formula for the volume of a cube: \(Volume = (side)^{3}\). Volume = \((1.500 \mathrm{~cm})^{3}\)
02

Calculate the density of the osmium cube

Density is defined as mass per unit volume: \(Density = \frac{mass}{volume}\) Given mass of the osmium cube = 76.31 g Volume of the osmium cube = \((1.500\,\text{cm})^3\) Density = \(\frac{76.31\,\text{g}}{(1.500\,\text{cm})^3}\) (b) To find the mass of titanium metal that displaces 125.0 mL of water:
03

Calculate the volume of titanium in cm³

We are given the volume of water displaced by the titanium, which is equal to the volume of the titanium itself. Volume of titanium = 125.0 mL (since 1 cm³ = 1 mL) Volume of titanium = 125.0 cm³
04

Calculate the mass of the titanium

Given, the density of titanium is 4.51 g/cm³ Density = \(\frac{mass}{volume}\) We need to find the mass. So, mass = Density × Volume Mass of Titanium = (4.51 g/cm³) × (125.0 cm³) (c) To find the mass of 0.1500 L of benzene at 15°C:
05

Convert the volume of benzene to mL

Given volume of benzene = 0.1500 L We know that 1 L = 1000 mL Volume of benzene = 0.1500 × 1000 mL
06

Calculate the mass of benzene

Given, the density of benzene at 15°C is 0.8787 g/mL Density = \(\frac{mass}{volume}\) We need to find the mass. So, mass = Density × Volume Mass of benzene = (0.8787 g/mL) × (0.1500 × 1000 mL)

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Most popular questions from this chapter

Is the use of significant figures in each of the following statements appropriate? Why or why not? (a) Apple sold 22,727,000 iPods during the last three months of 2008 . (b) New York City receives 49.7 inches of rain, on average, per year. (c) In the United States, \(0.621 \%\) of the population has the surname Brown. (d) You calculate your grade point average to be \(3.87562 .\)

The concepts of accuracy and precision are not always easy to grasp. Here are two sets of studies: (a) The mass of a secondary weight standard is determined by weighing it on a very precise balance under carefully controlled laboratory conditions. The average of 18 different weight measurements is taken as the weight of the standard. (b) A group of 10,000 males between the ages of 50 and 55 is surveyed to ascertain a relationship between calorie intake and blood cholesterol level. The survey questionnaire is quite detailed, asking the respondents about what they eat, smoke, drink, and so on. The results are reported as showing that for men of comparable lifestyles, there is a \(40 \%\) chance of the blood cholesterol level being above \(230 \mathrm{mg} / \mathrm{dL}\) for those who consume more than 40 calories per gram of body weight per day, as compared with those who consume fewer than 30 calories per gram of body weight per day. Discuss and compare these two studies in terms of the precision and accuracy of the result in each case. How do the two studies differ in ways that affect the accuracy and precision of the results? What makes for high precision and accuracy in any given study? In each of these studies, what factors might not be controlled that could affect the accuracy and precision? What steps can be taken generally to attain higher precision and accuracy?

a) The temperature on a warm summer day is \(87^{\circ} \mathrm{F}\). What is the temperature in \({ }^{\circ} \mathrm{C} ?\) (b) Many scientific data are reported at \(25^{\circ} \mathrm{C}\). What is this temperature in kelvins and in degrees Fahrenheit? (c) Suppose that a recipe calls for an oven temperature of \(400{ }^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius and to kelvins. (d) Liquid nitrogen boils at \(77 \mathrm{~K}\). Convert this temperature to degrees Fahrenheit and to degrees Celsius.

Suggest a method of separating each of the following mixtures into two components: (a) sugar and sand, (b) oil and vinegar.

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