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Chapter 3: Problem 35

(a) What is the mass, in grams, of \(2.50 \times 10^{-3}\) mol of ammonium phosphate? (b) How many moles of chloride ions are in \(0.2550 \mathrm{~g}\) of aluminum chloride? (c) What is the mass, in grams, of \(7.70 \times 10^{20}\) molecules of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\) (d) What is the molar mass of cholesterol if \(0.00105 \mathrm{~mol}\) weighs \(0.406 \mathrm{~g}\) ?

Short Answer

Expert verified
(a) The mass of \(2.50 \times 10^{-3}\) mol of ammonium phosphate is 0.373 g. (b) There are \(5.73 \times 10^{-3}\) moles of chloride ions in 0.2550 g of aluminum chloride. (c) The mass of \(7.70 \times 10^{20}\) molecules of caffeine is 0.249 g. (d) The molar mass of cholesterol is 386.67 g/mol.

Step by step solution

01

(a) Find molar mass of Ammonium Phosphate

To find the mass, we first have to find the molar mass of ammonium phosphate, which has the formula (NH4)3PO4. The molar mass of N = 14.01 g/mol The molar mass of H = 1.01 g/mol The molar mass of P = 30.97 g/mol The molar mass of O = 16.00 g/mol The molar mass of ammonium phosphate is: \((3 * 14.01) + (12 * 1.01) + 30.97 + (4 * 16.00) = 149.09 \mathrm{~g/mol}\)
02

(a) Find mass

Now we can find the mass, by multiplying the given moles with the molar mass of ammonium phosphate. Mass = moles * molar mass Mass = \(2.50 \times 10^{-3}\) mol * 149.09 g/mol = 0.373 g
03

(b) Moles of Aluminum Chloride

First find the molar mass of aluminum chloride, AlCl3. The molar mass of Al = 26.98 g/mol The molar mass of Cl = 35.45 g/mol Molar mass of AlCl3 = 26.98 + (3 * 35.45) = 133.33 g/mol Now find the moles of aluminum chloride given the mass. Moles = mass / molar mass Moles = \(0.2550 \mathrm{~g} / 133.33 \mathrm{~g/mol}\) = \(1.91 \times 10^{-3}\) mol
04

(b) Moles of Chloride

In 1 mol of AlCl3, there are 3 moles of chloride ions (Cl-). Therefore, the moles of chloride ions in \(1.91 \times 10^{-3}\) mol of AlCl3 is: \((1.91 \times 10^{-3} \mathrm{~mol}) * 3 = 5.73 \times 10^{-3} \mathrm{~mol}\)
05

(c) Molar mass and moles of Caffeine

First, find the molar mass of caffeine, C8H10N4O2. Molar mass of C = 12.01 g/mol Molar mass of N = 14.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of caffeine = \((8 * 12.01) + (10 * 1.01) + (4 * 14.01) + (2 * 16.00) = 194.19 \mathrm{~g/mol}\) Now, find the moles of caffeine from the given number of molecules, using Avogadro's number (\(6.022 \times 10^{23} \mathrm{~mol^{-1}}\)). Moles = number of molecules / Avogadro's number Moles = \(7.70 \times 10^{20}\) molecules / \(6.022 \times 10^{23} \mathrm{~mol^{-1}}\) = \(1.28 \times 10^{-3} \mathrm{~mol}\)
06

(c) Mass of Caffeine

Now, find the mass from the moles and molar mass of caffeine. Mass = moles * molar mass Mass = \(1.28 \times 10^{-3} \mathrm{~mol} * 194.19 \mathrm{~g/mol}\) = 0.249 g
07

(d) Molar Mass of Cholesterol

Use the provided mass and moles of cholesterol to find its molar mass. Molar mass = mass / moles Molar mass = \(0.406 \mathrm{~g} / 0.00105 \mathrm{~mol}\) = 386.67 g/mol

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Most popular questions from this chapter

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, which are principally \(\mathrm{N}_{2}(\sim 79 \%)\) and \(\mathrm{O}_{2}(\sim 20 \%)\). In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NOx" gases. In 2004, the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{\mathrm{x}}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\) into \(\mathrm{CO}_{2}\) and water. If \(85 \%\) of the oxygen in an engine is used to combust octane, and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of 500 grams of octane.

Write balanced chemical equations to correspond to each of the following descriptions: (a) Solid calcium carbide, \(\mathrm{CaC}_{2}\), reacts with water to form an aqueous solution of calcium hydroxide and acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\). (b) When solid potassium chlorate is heated, it decom-

Balance the following equations: (a) \(\mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)\) (b) \(\mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(\bar{l}) \longrightarrow \mathrm{HNO}_{3}(a q)\) (c) \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+\mathrm{HCl}(g)\) (d) \(\mathrm{Al}_{4} \mathrm{C}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{CH}_{4}(g)\) (e) \(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (f) \(\mathrm{Fe}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (g) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow\) \(\mathrm{MgSO}_{4}(a q)+\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(a q)\)

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (b) barium carbonate decomposes into barium axide and carbon dioxide gas when heated; (c) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l)\), is combusted in air; (d) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g)\), is combusted in air.

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