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Chapter 3: Problem 36

Calculate the following quantities: $$ \begin{array}{l}{\text { (a) mass, in grams, of } 1.50 \times 10^{-2} \text { mol CdS }} \\ {\text { (b) number of moles of } \mathrm{NH}_{4} \mathrm{Cl} \text { in } 86.6 \mathrm{g} \text { of this substance }} \\ {\text { (c) number of molecules in } 8.447 \times 10^{-2} \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{6}} \\ {\text { (d) number of } \mathrm{O} \text { atoms in } 6.25 \times 10^{-3} \mathrm{mol} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}}\end{array} $$

Short Answer

Expert verified
The short answer for this question is as follows: (a) The mass of 1.50x10^{-2} mol CdS is 2.1712 g. (b) The number of moles of NH4Cl in 86.6 g is 1.00029 mol. (c) The number of molecules in 8.447x10^{-2} mol C6H6 is 5.081x10^{22} molecules. (d) The number of O atoms in 6.25x10^{-3} mol Al(NO3)3 is 3.387x10^{22} O atoms.

Step by step solution

01

Find the molar mass of CdS

To find the mass of CdS, we first need to find the molar mass of CdS. The molar mass of an element is the mass of one mole of that substance, expressed in grams per mole. The molar mass of CdS can be calculated by adding the molar mass of Cd (cadmium) with the molar mass of S (sulfur). Molar mass of cd=112.41g/mol and S=32.07g/mol
02

Calculate the mass of CdS

Now that we have the molar mass, we can calculate the mass by using the given moles. Use this formula: mass = moles x molar_mass Mass = 1.5x10^{-2} mol CdS * (112.41g/mol + 32.07g/mol) = 2.1712 g Part (b) - Number of moles of NH4Cl in 86.6 g
03

Find the molar mass of NH4Cl

We need to find the molar mass of NH4Cl. The molar mass of NH4Cl can be calculated by adding the molar masses of N (nitrogen), H (hydrogen) x 4, and Cl (chlorine). Molar mass of NH4Cl = 14.01g/mol + 1.01g/mol * 4 + 35.45g/mol
04

Calculate the number of moles of NH4Cl

Now that we have the molar mass, use the formula: moles = mass / molar_mass Moles = 86.6 g / (14.01g/mol + 1.01g/mol * 4 + 35.45g/mol) = 1.00029 mol NH4Cl Part (c) - Number of molecules in 8.447x10^{-2} mol C6H6
05

Use Avogadro's number to find the number of molecules

We are given the moles, and now we want to find the number of molecules. To do this, we will use Avogadro's number, which is 6.022x10^{23} molecules/mol. Then, use this formula: molecules = moles * Avogadro's_number Molecules = 8.447x10^{-2} mol C6H6 * 6.022x10^{23} molecules/mol = 5.081x10^{22} molecules C6H6 Part (d) - Number of O atoms in 6.25x10^{-3} mol Al(NO3)3
06

Determine the moles of O atoms

In each molecule of Al(NO3)3, there are three nitrate ions, and each nitrate ion (NO3) has one oxygen atom. Therefore, there are three oxygen atoms for each molecule of Al(NO3)3. To find the moles of oxygen atoms in 6.25x10^{-3} mol Al(NO3)3, use this formula: moles_O = (moles_Al(NO3)3) * (number of oxygen atoms per molecule) Moles_O = 6.25x10^{-3} mol Al(NO3)3 * 3 * 3 = 0.05625 mol O
07

Calculate the number of O atoms

Now that we have the moles of oxygen atoms, use Avogadro's number again to find the number of O_atoms: O_atoms = moles_O * Avogadro's_number O_atoms = 0.05625 mol O * 6.022x10^{23} molecules/mol = 3.387x10^{22} O atoms

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Most popular questions from this chapter

A chemical plant uses electrical energy to decompose aqueous solutions of NaCl to give \(\mathrm{Cl}_{2}, \mathrm{H}_{2},\) and \(\mathrm{NaOH} :\) $$ 2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) $$ If the plant produces \(1.5 \times 10^{6} \mathrm{kg}\left(1500\) metric tons) of \(\mathrm{Cl}_{2}\right.\) daily, estimate the quantities of \(\mathrm{H}_{2}\) and \(\mathrm{NaOH}\) produced.

(a) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is \(\mathrm{CgH}_{8} \mathrm{O}_{4} .\) How many moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in a \(0.500-\mathrm{g}\) tablet of aspirin? Assume the tablet is composed entirely of aspirin. (b) How many molecules of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in this tablet? (c) How many carbon atoms are in the tablet?

If \(1.5 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}, 1.5 \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8},\) and 1.5 \(\mathrm{mol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{3}\) are completely combusted in oxygen, which produces the largest number of moles of \(\mathrm{H}_{2} \mathrm{O} ?\) Which produces the least? Explain.

Solutions of sulfuric acid and lead(II) acetate react to form solid lead(II) sulfate and a solution of acetic acid. If 5.00 g of sulfuric acid and 5.00 g of lead(II) acetate are mixed, calculate the number of grams of sulfuric acid, lead(II) acetate, lead(II) sulfate, and acetic acid present in the mixture after the reaction is complete.

If Avogadro's number of pennies is divided equally among the 321 million men, women, and children in the United States, how many dollars would each receive? How does this compare with the gross domestic product (GDP) of the United States, which was \(\$ 17.419\) trillion in 2015\(?\) (The GDP is the total market value of the nation's goods and services.)
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