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Chapter 3: Problem 36

(a) What is the mass, in grams, of \(1.223 \mathrm{~mol}\) of iron(III) sulfate? (b) How many moles of ammonium ions are in \(6.955 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(1.50 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} ?\) (d) What is the molar mass of diazepam (Valium \(^{\circ}\) ) if 0.05570 mol has a mass of \(15.86 \mathrm{~g}\) ?

Short Answer

Expert verified
(a) The mass of $1.223\, \text{mol}$ of iron(III) sulfate is \(\boldsymbol{399.95 \, \text{g}}\). (b) There are \(\boldsymbol{0.2688\, \text{mol}}\) of ammonium ions in $6.955\, \text{g}$ of ammonium carbonate. (c) The mass of $1.50 \times 10^{21}$ molecules of aspirin is \(\boldsymbol{6.009 \, \text{g}}\). (d) The molar mass of diazepam is \(\boldsymbol{284.8 \, \text{g/mol}}\).

Step by step solution

01

Find the molar mass of iron(III) sulfate

To find the mass of iron(III) sulfate, we first need to find its molar mass. Iron(III) sulfate has the chemical formula Fe2(SO4)3. It consists of two Fe atoms, three SO4 units, totaling nine O atoms and three S atoms. To calculate the molar mass of Iron(III) sulfate, multiply the number of atoms of each element by their atomic weights and sum them: \(Molar \, mass = 2 \times (molar \, mass \, of \, Fe) + 3 \times [4 \times (molar \, mass \, of \, O) + (molar \, mass \, of \, S)]\)
02

Calculate the mass of iron(III) sulfate

To calculate the mass of iron(III) sulfate, multiply the given moles by its molar mass: \( Mass = Moles \times Molar \, mass \) #Problem (b)#
03

Obtain the molar mass of ammonium carbonate and calculate moles

Ammonium carbonate has the formula (NH4)2CO3. To calculate the required moles of ammonium ions, first, we find the molar mass of ammonium carbonate and then find the moles of the compound: \( Moles = \frac{Mass}{Molar \, mass} \) Finally, we can determine the moles of ammonium ions in the given mass of ammonium carbonate. #Problem (c)#
04

Find the molar mass of aspirin

Aspirin has the chemical formula C9H8O4. To find the molar mass of aspirin, we multiply the number of atoms of each element by their atomic weights and sum them: \( Molar \, mass \, of \, aspirin = 9 \times (molar \, mass \, of \, C) + 8 \times (molar \, mass \, of \, H) + 4 \times (molar \, mass \, of \, O) \)
05

Calculate the number of moles and mass of aspirin

First, we need to determine the number of moles to calculate the mass of aspirin: \( Number \, of \, moles = \frac{Number \, of \, particles}{Avogadro's \, number}\) Once we have the number of moles, we can find the mass of aspirin using the following formula: \( Mass = Moles \times Molar \, mass \) #Problem (d)#
06

Calculate the molar mass of diazepam

For diazepam, we are given the mass and the number of moles. We can simply find the molar mass using the formula: \( Molar \, mass = \frac{Mass}{Moles} \)

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Most popular questions from this chapter

Write a balanced chemical equation for the reaction that occurs when (a) calcium metal undergoes a combination reaction with \(\mathrm{O}_{2}(g) ;\) (b) copper(II) hydroxide decomposes into copper(II) oxide and water when heated; (c) heptane, \(\mathrm{C}_{7} \mathrm{H}_{16}(l),\) burns in air; (d) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l)\) burns in air.

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, 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 \(\mathrm{NO}\) 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 " \(\mathrm{NO}_{\mathrm{x}}^{\prime \prime}\) gases. In \(2007,\) the United States emitted an estimated 22 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.

The complete combustion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), the main component of gasoline, proceeds as follows: \(2 \mathrm{C}_{8} \mathrm{H}_{18}(l)+25 \mathrm{O}_{2}(g) \longrightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g)\) (a) How many moles of \(\mathrm{O}_{2}\) are needed to burn \(1.50 \mathrm{~mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18} ?\) (b) How many grams of \(\mathrm{O}_{2}\) are needed to burn \(10.0 \mathrm{~g}\) of \(\mathrm{C}_{8} \mathrm{H}_{18} ?\) (c) Octane has a density of \(0.692 \mathrm{~g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\). How many grams of \(\mathrm{O}_{2}\) are required to burn \(15.0 \mathrm{gal}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\) (the capacity of an average fuel tank)? (d) How many grams of \(\mathrm{CO}_{2}\) are produced when 15.0 gal of \(\mathrm{C}_{8} \mathrm{H}_{18}\) are combusted?

A manufacturer of bicycles has 4815 wheels, 2305 frames, and 2255 handlebars. (a) How many bicycles can be manufactured using these parts? (b) How many parts of each kind are left over? (c) Which part limits the production of bicycles?

(a) What is the mass, in grams, of \(2.50 \times 10^{-3} \mathrm{~mol}\) 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 \(0.00105 \mathrm{~mol}\) has a mass of \(0.406 \mathrm{~g} ?\)
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