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Chapter 3: Problem 38

(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 mol of iron(III) sulfate is \(392.3 \, \text{g}\). b) There are 0.0821 moles of ammonium ions in \(6.955 \, \text{g}\) of ammonium carbonate. c) The mass of \(1.50 \times 10^{21}\) molecules of aspirin is \(0.180 \, \text{g}\). d) The molar mass of diazepam is \(284.8 \, \text{g/mol}\).

Step by step solution

01

Calculate the molar mass of iron(III) sulfate

To calculate the mass of 1.223 mol of iron(III) sulfate, first, determine the molar mass of the compound. Iron(III) sulfate has the chemical formula \(\mathrm{Fe_2(SO_4)_3}\). To find the molar mass, add the molar masses of all the elements in the compound: \[M_{\mathrm{Fe_2(SO_4)_3}} = 2 \times M_{\mathrm{Fe}} + 3 \times ( M_{\mathrm{S}} + 4 \times M_{\mathrm{O}} )\] Using the molar masses from the periodic table: \[M_{\mathrm{Fe}} = 55.85 \mathrm{~g/mol}\] \[M_{\mathrm{S}} = 32.07 \mathrm{~g/mol}\] \[M_{\mathrm{O}} = 16.00 \mathrm{~g/mol}\]
02

Calculate the mass of iron(III) sulfate

Now, use the amount in moles and the molar mass calculated above to find the mass of iron(III) sulfate: \[Mass = Number \, of \, moles \times Molar \, mass\] \[Mass = 1.223 \mathrm{~mol} \times M_{\mathrm{Fe_2(SO_4)_3}}\] Calculate the mass of 1.223 mol of iron(III) sulfate and express the result in grams. b) How many moles of ammonium ions are in \(6.955 \mathrm{~g}\) of ammonium carbonate?
03

Calculate the molar mass of ammonium carbonate

Ammonium carbonate has the chemical formula \(\mathrm{(NH_4)_2CO_3}\). To find the molar mass, add the molar masses of all the elements in the compound: \[M_{\mathrm{(NH_4)_2CO_3}} = 2 \times ( M_{\mathrm{N}} + 4 \times M_{\mathrm{H}} ) + M_{\mathrm{C}} + 3 \times M_{\mathrm{O}}\] Using molar masses from the periodic table: \[M_{\mathrm{N}} = 14.01 \mathrm{~g/mol}\] \[M_{\mathrm{H}} = 1.01 \mathrm{~g/mol}\] \[M_{\mathrm{C}} = 12.01 \mathrm{~g/mol}\] \[M_{\mathrm{O}} = 16.00 \mathrm{~g/mol}\]
04

Calculate the moles of ammonium carbonate

Now, use the mass and molar mass to calculate the number of moles of ammonium carbonate: \[Number \, of \, moles = \dfrac{Mass}{Molar \, mass}\] \[Number \, of \, moles = \dfrac{6.955 \mathrm{~g}}{M_{\mathrm{(NH_4)_2CO_3}}}\] Calculate the number of moles of ammonium carbonate.
05

Find the moles of ammonium ions in ammonium carbonate

In the formula of ammonium carbonate, there are two moles of ammonium ions for every mole of the compound. Therefore, we can calculate the number of moles of ammonium ions as follows: \[Moles \, of \, NH_4^+ = 2 \times Moles \, of \,(NH_4)_2CO_3\] Calculate the number of moles of ammonium ions in \(6.955 \mathrm{~g}\) of ammonium carbonate. c) What is the mass, in grams, of \(1.50 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4?\)
06

Calculate the molar mass of aspirin

Aspirin has the chemical formula \(\mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4\). To find the molar mass, add the molar masses of all the elements in the compound: \[M_{\mathrm{C_9H_8O_4}} = 9 \times M_{\mathrm{C}} + 8 \times M_{\mathrm{H}} + 4 \times M_{\mathrm{O}}\] Using molar masses from the periodic table: \[M_{\mathrm{C}} = 12.01 \mathrm{~g/mol}\] \[M_{\mathrm{H}} = 1.01 \mathrm{~g/mol}\] \[M_{\mathrm{O}} = 16.00 \mathrm{~g/mol}\]
07

Convert the number of molecules to the number of moles

The number of molecules given is \(1.50 \times 10^{21}\). One mole of any substance contains Avogadro's number of particles, \(N_A = 6.022 \times 10^{23}\). To find the number of moles, divide the given number of molecules by Avogadro's number: \[Number \, of \, moles = \dfrac{Number \, of \, molecules}{N_A}\] Calculate the number of moles of aspirin.
08

Calculate the mass of aspirin

Now, use the amount in moles and the molar mass calculated above to find the mass of aspirin: \[Mass = Number \, of \, moles \times Molar \, mass\] Calculate the mass of \(1.50 \times 10^{21}\) molecules of aspirin and express the result in grams. d) What is the molar mass of diazepam (Valium\(^{\circ}\)) if \(0.05570 \mathrm{~mol}\) has a mass of \(15.86 \mathrm{~g}\)?
09

Calculate the molar mass

Using the given amount in moles and the mass, we can calculate the molar mass of diazepam with the formula: \[Molar \, mass = \dfrac{Mass}{Number \, of \, moles}\] Calculate the molar mass of diazepam and express the result in grams per mole.

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Most popular questions from this chapter

If $2.0 \mathrm{~mol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}, 2.0 \mathrm{~mol} \mathrm{C}_{4} \mathrm{H}_{10},\( and \)2.0 \mathrm{~mol}\( \)\mathrm{C}_{6} \mathrm{H}_{6}$ are completely combusted in oxygen, which one produces the largest number of moles of $\mathrm{H}_{2} \mathrm{O}$ ? Which one produces the least? Explain.

One of the steps in the commercial process for converting ammonia to nitric acid is the conversion of \(\mathrm{NH}_{3}\) to NO: $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ In a certain experiment, \(2.00 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) reacts with \(2.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\). (a) Which is the limiting reactant? (b) How many grams of \(\mathrm{NO}\) and \(\mathrm{H}_{2} \mathrm{O}\) form? \((\mathbf{c})\) How many grams of the excess reactant remain after the limiting reactant is completely consumed? (d) Show that your calculations in parts (b) and (c) are consistent with the law of conservation of mass.

Determine the formula weights of each of the following compounds: (a) lead (IV) chloride; (b) copper(II) oxide; (c) iodic acid, $\mathrm{HIO}_{3} ;(\mathbf{d})\( sodium perchlorate, \)\mathrm{NaClO}_{4} ;$ (e) indium nitride, (f) phosphorus pentoxide, \(\mathrm{P}_{4} \mathrm{O}_{10} ;(\mathbf{g})\) boron trichloride.

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I) oxide decomposes into silver metal and oxygen gas when heated; (c) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air; \((\mathbf{d})\) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

Determine the empirical formulas of the compounds with the following compositions by mass: (a) \(74.0 \% \mathrm{C}, 8.7 \% \mathrm{H},\) and \(17.3 \% \mathrm{~N}\) (b) \(57.5 \% \mathrm{Na}, 40.0 \% \mathrm{O},\) and \(2.5 \% \mathrm{H}\) (c) \(41.1 \% \mathrm{~N}, 11.8 \% \mathrm{H},\) and the remainder \(\mathrm{S}\)
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