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Chapter 1: Problem 36

(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 L of benzene at this temperature.

Short Answer

Expert verified
a) The density of the osmium metal cube is approximately \(22.6\, \dfrac{g}{\text{cm}^3}\). b) The mass of titanium that displaces 125.0 mL of water is approximately 563.8 g. c) The mass of 0.1500 L of benzene at 15°C is approximately 131.81 g.

Step by step solution

01

(1) Calculate the density of the osmium metal cube

We are given the dimensions and mass of an osmium metal cube. We need to find its density. To do this, we will first find the volume of the cube and then use the formula for density. The volume of a cube can be calculated using the formula: Volume = Side^3 The side length of the cube is given as 1.500 cm. So, the volume of the cube is: Volume = (1.500 cm)^3 = \(1.500^3\) cm³ ≈ 3.375 cm³ Now, we can use the formula for density: Density = Mass / Volume We know the mass of the cube is 76.31 g. So, the density of the osmium metal cube is: Density = 76.31 g / 3.375 cm³ ≈ \(22.6\, \dfrac{g}{\text{cm}^3}\)
02

(2) Calculate the mass of titanium that displaces 125.0 mL of water

We are given the density of titanium metal as 4.51 g/cm³ at 25°C. We need to find the mass of titanium that displaces 125.0 mL of water. First, we need to convert mL to cm³ (1 mL = 1 cm³). So, the volume of water displaced is 125 cm³. We know the density of titanium is 4.51 g/cm³. To find the mass of titanium, we rearrange the formula for density: Mass = Density x Volume Now we can plug in the values: Mass = 4.51 g/cm³ × 125 cm³ ≈ \(563.8\, g\)
03

(3) Calculate the mass of 0.1500 L of benzene at 15°C

The density of benzene at 15°C is given as 0.8787 g/mL. We need to find the mass of 0.1500 L of benzene. First, we need to convert L to mL (1 L = 1000 mL). So, the volume of benzene is 150 mL. Now, we can use the formula for density: Density = Mass / Volume We can rearrange the formula to find the mass of benzene: Mass = Density x Volume Now we can plug in the values: Mass = 0.8787 g/mL × 150 mL ≈ \(131.81\, g\) In summary: a) The density of the osmium metal cube is approximately \(22.6\, \dfrac{g}{\text{cm}^3}\). b) The mass of titanium that displaces 125.0 mL of water is approximately 563.8 g. c) The mass of 0.1500 L of benzene at 15°C is approximately 131.81 g.

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