1.2 - The Mole Concept

Which of the following statements does not conform to the definition of a mole?

• A.$\hspace{1em}$ 1 mole is the number of H$_{2}$O molecules in 18.02 g of H$_{2}$O

• B.$\hspace{1em}$ 1 mole of Fe has a mass equal to the relative atomic mass of Fe in grams

• C.$\hspace{1em}$ 1 mole of any substance contains 6.02 $\times$ 10$^{23}$ particles

• D.$\hspace{1em}$ 1 mole is the number of H$_{2}$ molecules in 1.01 g of $\ce{H2}$

Which compound has the largest molar mass?

• A.$\hspace{1em}$ $\ce{FeSO4}$

• B.$\hspace{1em}$ $\ce{K2Cr2O7}$

• C.$\hspace{1em}$ $\ce{KMnO4}$

• D.$\hspace{1em}$ $\ce{(NH4)3PO4}$

Which of the following statements is true?

• A.$\hspace{1em}$ The empirical formula shows only the type of each atom in a molecule.

• B.$\hspace{1em}$ The molecular formula is always the same as the empirical formula.

• C.$\hspace{1em}$ Organic molecules often have different empirical and molecular formulas.

• D.$\hspace{1em}$ The empirical formula is always greater than the molecular formula.

Calculate the number of moles in $20.5$ grams of sodium phosphate ($\ce{Na3PO4}$).

• A.$\hspace{1em}$ 0.125 mol

• B.$\hspace{1em}$ 1.25 mol

• C.$\hspace{1em}$ 12.5 mol

• D.$\hspace{1em}$ 125 mol

Which of the following substances would have the lowest mass?

• A.$\hspace{1em}$ 2.50 $\textit{moles}\$ H$_2$O

• B.$\hspace{1em}$ 2.50 $\textit{moles}$ CH$_4$

• C.$\hspace{1em}$ 2.00 $\textit{moles}$ SO$_2$

• D.$\hspace{1em}$ 2.00 $\textit{moles}$ CO$_2$

Bromine has 2 stable isotopes: bromine-79 and bromine-81. What is the relative atomic mass of bromine (Br)?

Isotope	Relative Abundance	Atomic Mass
$^{79}$Br	50.69%	78.92
$^{81}$Br	49.31%	80.92

• A.$\hspace{1em}$ 78.5

• B.$\hspace{1em}$ 80.1

• C.$\hspace{1em}$ 81.2

• D.$\hspace{1em}$ 79.9

How many molecules are there in 4.80 $\textit{moles}$ of glucose?

• A.$\hspace{1em}$ 2.89 $\times$ 10$^{24}$ molecules

• B.$\hspace{1em}$ 2.50 $\times$ 10$^{24}$ molecules

• C.$\hspace{1em}$ 3.50 $\times$ 10$^{24}$ molecules

• D.$\hspace{1em}$ 2.59 $\times$ 10$^{24}$ molecules

[Maximum mark: 5]

Eugenol is an oily, aromatic liquid extracted from essential oils such as clove and cinnamon. The molecular formula of eugenol is C$_{10}$H$_{12}$O$_{2}$.

1. Calculate the molar mass of eugenol. [1]
   

2. Determine the percentage by mass of carbon, hydrogen, and oxygen in eugenol. [3]
   

3. Predict the simplest, whole-number ratio of the atoms in eugenol. [1]
   

What is the percentage by mass of S in the compound sulfur dioxide $\ce{SO2}$?

• A.$\hspace{1em}$ 25%

• B.$\hspace{1em}$ 50%

• C.$\hspace{1em}$ 75%

• D.$\hspace{1em}$ 100%

When a solution of lead (II) nitrate is mixed with a solution of potassium hydroxide, a precipitate containing lead (II) ions forms.

Which ions are considered to be the spectator ions?

• A. $\hspace{1em}$ Pb$^{2+}$, NO$_3^-$

• B. $\hspace{1em}$ K$^+$, OH$^-$

• C. $\hspace{1em}$ Pb$^{2+}$, OH$^-$

• D. $\hspace{1em}$ K$^+$, NO$_3^-$

[Maximum mark: 6]

Ascorbic acid (C$_{6}$H$_{8}$O$_{6}$), or vitamin C, is a water-soluble vitamin that is essential for our immune system.

1. Calculate the number of moles in 2.50 $\textit{g}$ of ascorbic acid. [1]
   

2. Calculate the mass of 1.28 $\textit{moles}$ of ascorbic acid. [1]
   

3. Calculate the number of molecules in 50.0 $\textit{g}$ of ascorbic acid. [2]
   

4. Determine the number of moles of carbon in 225 $\textit{mg}$ of ascorbic acid [2]
   

[Maximum mark: 15]

A solution of an unknown hydrate of calcium chlorate (Ca(ClO$_3$)$_2$ $\cdotp$ n H$_2$O) is made by dissolving 4.164 $g$ in 150.0 cm$^3$ of water. The resulting solution of calcium chlorate has a concentration of 0.1142 $mol \ dm^{-3}$.

1. 1. Determine the number of moles and the mass of calcium chlorate present in the solution. [2]
      

   2. Determine the mass of water and then the number of moles of water that was present in the hydrate used to make the original solution. [2]
      

   3. Determine the value of n in the hydrate formula, Ca(ClO$_3$)$_2$ $\cdotp$ n H$_2$O. [1]
      

2. The calcium chlorate solution made above is then mixed with 200.0 $cm^3$ of $0.07500 \ mol \ dm^{-3}$ sodium phosphate (Na$_3$PO$_4$ ), producing a precipitate of calcium phosphate, Ca$_3$(PO$_4$)$_2$.

   1. Write the net ionic equation for this reaction, including state symbols. [2]
      

   2. Determine the limiting reactant in this reaction, showing your work. [2]
      

   3. If 1.535 $g$ of calcium phosphate is recovered, determine the percent yield in this reaction. [3]
      

   4. Determine the concentration of phosphate ions remaining in the solution after removing the precipitate, assuming that is the only loss of phosphate ions. [3]
      

[Maximum mark: 7]

Lipoic acid is an antioxidant that can be taken as a supplement for the body.

1. Determine the empirical formula of lipoic acid. [4]
   

Element	Percentage Composition by mass
C	46.56%
H	6.85%
O	15.5%
S	31.08%

2. Calculate the molar mass of the empirical formula of lipoic acid. [1]
   

3. If the actual molar mass of lipoic acid is 206.44 $\textit{g} \ mol^{-1}$, determine its molecular formula. [2]
   

[Maximum mark: 10]

Copper(II) chloride can exist as an anhydrous solid or hydrate.

1. A $1.78\ g$ sample of copper(II) chloride hydrate was heated on a watch glass until the blue solid changed completely to brown, and the following data was recorded:

   Mass of watch glass ($g$)	$24.57 \pm 0.01$
   Mass of copper(II) chloride hydrate ($g$)	$1.78 \pm 0.01$
   Mass of anhydrous copper(II) chloride + watch glass (1st heating, 5 min)	$26.03 \pm 0.01$
   Mass of anhydrous copper(II) chloride + watch glass (2nd heating, 5 min)	$25.99 \pm 0.01$
   Mass of anhydrous copper(II) chloride + watch glass (3rd heating, 2 min)	$25.99 \pm 0.01$

   Suggest a reason why the sample was heated for a second 5 minute increment showing a mass change. [1]
   

2. Calculate the mass of anhydrous copper(II) chloride. Do not include the calculations of uncertainties in your work. [1]
   

3. Calculate the mass of water in the hydrated copper(II) chloride sample. Do not include the calculations of uncertainties in your work. [1]
   

4. Calculate the percent uncertainty on the mass of water in the copper(II) chloride sample. [2]
   

5. Determine the chemical formula for the copper(II) chloride hydrate from the experimental data. [3]
   

6. State the chemical name of the copper(II) chloride hydrate from this experiment. [1]
   

7. State the core electron configuration for copper. [1]
   

What mass of lead (II) carbonate would contain 20.7 $\textit{g}$ of lead?

• A.$\hspace{1em}$ 47.4 $\textit{g}$

• B.$\hspace{1em}$ 26.7 $\textit{g}$

• C.$\hspace{1em}$ 23.5 $\textit{g}$

• D.$\hspace{1em}$ 32.7 $\textit{g}$

[Maximum mark: 5]

A sample of 9.70 $\textit{g}$ of an unknown organic compound composed of carbon, hydrogen, and nitrogen was burnt with excess oxygen. The combustion produced nitrogen gas, 27.5 $\textit{g}$ of CO$_{2}$ and 6.57 $\textit{g}$ of H$_{2}$O.

1. Calculate the mass of nitrogen produced. [3]
   

2. Determine the empirical formula of the compound. [2]
   

What is the molecular formula of a compound with an empirical formula of $\ce{CH2O}$ and a molar mass of $180.18\ g\ mol^{-1}$?

• A. $\hspace{1em}$ $\ce{CH2O}$

• B. $\hspace{1em}$ $\ce{C6H6O6}$

• C. $\hspace{1em}$ $\ce{C6H12O6}$

• D. $\hspace{1em}$ $\ce{C5H10O5}$

[Maximum mark: 11]

Siderite is a mineral containing iron in the form of iron (II) carbonate, FeCO$_3$.

A 15.00 $g$ sample of impure siderite was ground into a fine powder and dissolved in 250.0 $cm^3$ of hot water, and then filtered to remove the insoluble components. After filtration, a 35.00 $cm^3$ sample of the iron solution was analyzed via redox titration using a 0.120 $mol \ dm^{-3}$ solution of potassium dichromate. The balanced redox equation is given below:

Cr$_2$O$_{7(aq)} ^{2-}$ + 14 H$^+_{(aq)}$ + 6 Fe$^{2+}_{(aq)}$ $\rightarrow$ 2 Cr$^{3+}_{(aq)}$ + 6 Fe$^{3+}_{(aq)}$ + 7 H$_2$O$_{(l)}$

1. 1. Calculate the theoretical percent composition of iron in a sample of pure siderite or iron (II) carbonate. [1]
      

   2. If 18.1 $cm^3$ of dichromate solution is used to titrate the actual iron sample to the equivalence point, calculate the number of moles of iron in the titrated sample. [2]
      

   3. Using your value from (ii), determine the mass of iron present in the original sample of siderite. [2]
      

   4. Using the experimental number of moles of $\ce{Fe^{2+}}$ found in (ii), calculate the experimental mass of iron carbonate (FeCO$_3$) in the impure sample and then calculate the percent of impurities found in this sample. [2]
      

2. Another iron-containing mineral is a hydrate of iron sulfate, Fe$_x$(SO$_4$)$_y$ $\cdotp$ $n H_2$O, pure sample is first heated to drive off all of the water. After heating to a consistent mass, a sample with a mass of 5.250 $g$ is found to have 3.561 $g$ of anhydrous material remaining. The remaining anhydrous material was analyzed and found to have 36.76$\%$ iron, 21.11$\%$ sulfur, and 42.13$\%$ oxygen.

   1. Determine the empirical formula of the anhydrate. [1]
      

   2. If the molar mass of the hydrate is determined to be 151.92 $g \ mol^{-1}$, what is the actual formula of the anhydrate? [1]
      

   3. Use the information given in part b(i) to determine the number of moles of water present and, thus, the formula of the hydrate. [2]
      

[Maximum mark: 14]

Aluminum and copper can react in redox reactions. One common reaction is between aluminum metal and copper(II) nitrate.

1. Write the balanced equation for the reaction of aluminum with copper(II) nitrate, including state symbols. [1]
   

2. The rate of this reaction can be measured using UV-Vis spectroscopy with the disappearance of the blue-green color of copper(II) nitrate when strips of solid aluminum are added to the solution.

   

   Calculate the instantaneous rate at $50\ s$ in units of $s^{-1}$ using the experimental data showing annotations on the graph above. [2]
   

3. Suggest two changes to the experiment that would increase the reaction rate. [2]
   

4. Using the graph below, deduce the order of reaction with respect to $\ce{Cu^2+}$. [1]
   

   

5. If the reaction is zero order with respect to $\ce{Al}$, state the rate expression for the reaction of $\ce{Al}$ with $\ce{Cu(NO3)2}$ and calculate the rate constant, specifying the correct units for $k$. [3]
   

6. If solid copper and solid aluminum were used to create a galvanic electrochemical cell, identify the following: [2]
   
   Anode material: ____________
   Cathode material: __________
   Half-reaction at the anode: _____________
   Half-reaction at the cathode: _____________

7. Identify the reducing and oxidizing agents in the aluminum and copper(II) nitrate reaction. [1]
   

8. Nitrate ions can also react in a redox reaction. An example of an unbalanced half-reaction for nitrate ions is $\ce{NO3- \to NO2-}$.

   Deduce the oxidation state of the nitrogen atom in $\ce{NO3-}$ and $\ce{NO2-}$. [1]
   

9. Deduce the balanced half redox reaction for $\ce{NO3- \to NO2-}$ in an acidic medium. [1]
   

[Maximum mark: 15]

Copper(II) chloride can exist as an anhydrous solid or hydrate.

1. A $1.78\ g$ sample of copper(II) chloride hydrate was heated on a watch glass until the blue solid changed completely to brown, and the following data was recorded:

   Masses	Value
   Mass of watch glass ($g$)	$24.57 \pm 0.01$
   Mass of copper(II) chloride hydrate ($g$)	$1.78 \pm 0.01$
   Mass of anhydrous copper(II) chloride + watch glass (1st heating, 5 min)	$26.03 \pm 0.01$
   Mass of anhydrous copper(II) chloride + watch glass (2nd heating, 5 min)	$25.99 \pm 0.01$
   Mass of anhydrous copper(II) chloride + watch glass (3rd heating, 2 min)	$25.99 \pm 0.01$

   Suggest a reason why the sample was heated for a second 5 min increment showing a mass change. [1]
   

2. Calculate the mass of anhydrous copper(II) chloride. Do not include the calculations of uncertainties in your work. [1]
   

3. Calculate the mass of water in the hydrated copper(II) chloride sample.Do not include the calculations of uncertainties in your work. [1]
   

4. Calculate the percent uncertainty on the mass of water in the copper(II) chloride sample. [2]
   

5. Determine the chemical formula for the copper(II) chloride hydrate from the experimental data. [3]
   

6. State the chemical name of the copper(II) chloride hydrate from this experiment. [1]
   

7. State the core electron configuration for copper. [1]
   

8. Copper is known to exist in complex ions. One such complex ion is $\ce{[Cu(H2O)6]^{2+}}$. State the molecular geometry around the central metal ion and the type of bonding that exists between the $\ce{Cu^{2+}}$ and the ligands. [2]
   

9. When $\ce{[Cu(H2O)6]^{2+}}$ reacts with ammonia, $\ce{NH3}$, the color changes from light to dark blue. Explain the cause of this color change using Sections 3 and 15 of the data booklet. [3]
   

[Maximum mark: 12]

Spectral analysis of molecules can be useful in identifying structure.

1. Determine the empirical formula of a molecule with the following percent composition by mass. [2]
   

   Element	$\%$ by mass
   C	$69.7\%$
   H	$11.7\%$
   O	$18.6\%$

2. State the molecular formula for this molecule if the mass spectrum indicates a molecular ion at $86\, m/z$. [1]
   

3. State the index of hydrogen deficiency for this molecule. [1]
   

4. An infrared spectrum was obtained for this molecule. Use Section 26 of the Data Booklet to identify two possible molecular structures consistent with the spectrum below. [2]
   

   [Source: Created with the NIST Chemistry WebBook - https:// webbook.nist.gov]

5. Explain why the infrared spectrum alone is not useful in confirming the identity of this molecule. [2]
   

6. The following data was collected from an $\ce{^1H}$ NMR spectrum of the molecule. Using Section 27 of the Data Booklet, explain how this data can distinguish between the molecules suggested in (d), stating the confirmed identity of the molecule. [2]
   

   Chemical shift ($ppm$)	Integration
   2.40	4
   1.06	6

7. Predict, with a reason, the spin-spin coupling that would be observed for the $\ce{^1H}$ NMR signal at 1.06 $ppm$. [2]