101. In a neutral compound, the sum of oxidation numbers of all atoms is:
ⓐ. equal to \(+1\)
ⓑ. equal to the number of atoms
ⓒ. equal to \(0\)
ⓓ. equal to the molar mass
Correct Answer: equal to \(0\)
Explanation: For a neutral compound, the algebraic sum of oxidation numbers of all atoms is \(0\). This rule is used to calculate unknown oxidation numbers in formulas such as \( \mathrm{CO_2} \), \( \mathrm{H_2SO_4} \), and \( \mathrm{Fe_2O_3} \). The sum is algebraic, so positive and negative values must be included with their signs. It is not related to molar mass or simply to the number of atoms. The total must match the overall charge of the species, and a neutral species has no net charge.
102. For a polyatomic ion, the sum of oxidation numbers of all atoms must equal:
ⓐ. \(0\) in every case
ⓑ. the charge on the ion
ⓒ. the number of oxygen atoms only
ⓓ. the total number of electrons in the ion
Correct Answer: the charge on the ion
Explanation: In a polyatomic ion, the sum of oxidation numbers equals the overall ionic charge. For example, in \( \mathrm{SO_4^{2-}} \), the sum of sulphur and four oxygen oxidation numbers is \(-2\). In \( \mathrm{NH_4^+} \), the sum is \(+1\). This extends the neutral-compound rule by replacing \(0\) with the actual ion charge. The sign of the ionic charge must be included in the equation.
103. In \( \mathrm{SO_4^{2-}} \), if oxygen is assigned \(-2\), the oxidation number of sulphur is:
ⓐ. \(+4\)
ⓑ. \(+5\)
ⓒ. \(+8\)
ⓓ. \(+6\)
Correct Answer: \(+6\)
Explanation: \( \textbf{Known value:} \) Oxygen is \(-2\) in \( \mathrm{SO_4^{2-}} \).
\( \textbf{Oxygen contribution:} \)
\[
4(-2) = -8
\]
\( \textbf{Ion charge rule:} \) The sum of oxidation numbers must equal \(-2\).
\( \textbf{Let sulphur be } x: \)
\[
x - 8 = -2
\]
\[
x = +6
\]
\( \textbf{Final answer:} \) Sulphur has oxidation number \(+6\). The ion charge \(-2\) belongs to the whole ion, not to each oxygen atom separately.
104. In \( \mathrm{NH_4^+} \), using \( \mathrm{H}=+1 \), the oxidation number of nitrogen is:
ⓐ. \(-3\)
ⓑ. \(-1\)
ⓒ. \(+3\)
ⓓ. \(+5\)
Correct Answer: \(-3\)
Explanation: \( \textbf{Known value:} \) Hydrogen is \(+1\) in \( \mathrm{NH_4^+} \).
\( \textbf{Hydrogen contribution:} \)
\[
4(+1)=+4
\]
\( \textbf{Ion charge rule:} \) The total oxidation-number sum must equal \(+1\).
\( \textbf{Let nitrogen be } x: \)
\[
x + 4 = +1
\]
\[
x = -3
\]
\( \textbf{Final answer:} \) Nitrogen has oxidation number \(-3\) in \( \mathrm{NH_4^+} \). The positive charge of the ion is the total charge of the whole ion, not the oxidation number of nitrogen.
105. A neutral compound has the formula \( \mathrm{X_2O_3} \). If oxygen is assigned \(-2\), the oxidation number of \( \mathrm{X} \) is:
ⓐ. \(+2\)
ⓑ. \(+3\)
ⓒ. \(+4\)
ⓓ. \(+6\)
Correct Answer: \(+3\)
Explanation: \( \textbf{Formula:} \) The compound is \( \mathrm{X_2O_3} \).
\( \textbf{Known oxidation number:} \) Oxygen is assigned \(-2\).
\( \textbf{Total contribution of oxygen:} \)
\[
3(-2)=-6
\]
\( \textbf{Neutral compound rule:} \) The total oxidation-number sum must be \(0\).
\( \textbf{Let the oxidation number of } \mathrm{X} \textbf{ be } x: \)
\[
2x-6=0
\]
\[
2x=6
\]
\[
x=+3
\]
\( \textbf{Final answer:} \) \( \mathrm{X} \) has oxidation number \(+3\). The subscript \(2\) multiplies the oxidation number of \( \mathrm{X} \), so it cannot be ignored.
106. The expression for finding the oxidation number of \( \mathrm{Cr} \) in \( \mathrm{Cr_2O_7^{2-}} \), taking oxygen as \(-2\), is:
ⓐ. \(2x+7(-2)=-2\)
ⓑ. \(x+7(-2)=-2\)
ⓒ. \(2x+7(-2)=0\)
ⓓ. \(x+2(-7)=-2\)
Correct Answer: \(2x+7(-2)=-2\)
Explanation: The ion \( \mathrm{Cr_2O_7^{2-}} \) contains two chromium atoms and seven oxygen atoms. If the oxidation number of each chromium atom is \(x\), the total chromium contribution is \(2x\). Oxygen contributes \(7(-2)\). Since the species is a polyatomic ion with charge \(-2\), the oxidation-number sum must equal \(-2\), not \(0\). The correct setup is \(2x+7(-2)=-2\), where both the chromium subscript and ion charge are included.
107. A calculation for \( \mathrm{MnO_4^-} \) is written as \(x+4(-2)=0\), giving \(x=+8\). The mistake is that:
ⓐ. oxygen should be \(+2\) in all oxoanions
ⓑ. the subscript \(4\) should not multiply oxygen
ⓒ. the ion charge \(-1\) was not used in the sum
ⓓ. manganese must always have oxidation number \(0\)
Correct Answer: the ion charge \(-1\) was not used in the sum
Explanation: \( \mathrm{MnO_4^-} \) is a polyatomic ion, not a neutral compound. The sum of oxidation numbers must therefore equal the ionic charge, \(-1\). Oxygen is normally \(-2\) here, so four oxygen atoms contribute \(4(-2)=-8\). The correct equation is \(x-8=-1\), giving \(x=+7\). Using \(0\) as the total would be valid for a neutral molecule, not for this ion.
108. In \( \mathrm{PO_4^{3-}} \), the oxidation number of phosphorus is:
ⓐ. \(+3\)
ⓑ. \(+4\)
ⓒ. \(+7\)
ⓓ. \(+5\)
Correct Answer: \(+5\)
Explanation: \( \textbf{Known value:} \) Oxygen is \(-2\) in \( \mathrm{PO_4^{3-}} \).
\( \textbf{Oxygen contribution:} \)
\[
4(-2)=-8
\]
\( \textbf{Ion charge condition:} \) The sum of oxidation numbers must equal \(-3\).
\( \textbf{Let phosphorus be } x: \)
\[
x-8=-3
\]
\[
x=+5
\]
\( \textbf{Final answer:} \) Phosphorus has oxidation number \(+5\). The charge \(-3\) belongs to the whole phosphate ion and must be used as the total on the right side.
109. Study the table and select the row in which the oxidation-number equation is properly written.
| Row | Species | Equation for unknown \(x\) |
|---|
| P | \( \mathrm{CO_3^{2-}} \) | \(x+3(-2)=-2\) |
| Q | \( \mathrm{NO_3^-} \) | \(x+3(-2)=0\) |
| R | \( \mathrm{SO_4^{2-}} \) | \(x+4(-2)=+2\) |
| S | \( \mathrm{ClO_3^-} \) | \(x+3(-2)=+1\) |
ⓐ. Row Q
ⓑ. Row R
ⓒ. Row P
ⓓ. Row S
Correct Answer: Row P
Explanation: In \( \mathrm{CO_3^{2-}} \), oxygen contributes \(3(-2)\), and the total must equal \(-2\), so Row P is properly written. Row Q treats \( \mathrm{NO_3^-} \) as if it were neutral, but its total should be \(-1\). Row R reverses the sign of the sulphate ion charge; it should be \(-2\), not \(+2\). Row S also uses the wrong total because \( \mathrm{ClO_3^-} \) has total charge \(-1\). The sign of the ion charge is as important as the numerical value.
110. A graph is described for a family of neutral compounds \( \mathrm{XO_n} \), where oxygen is \(-2\).
The x-axis shows \(n\), the number of oxygen atoms in \( \mathrm{XO_n} \). The y-axis shows the oxidation number of \( \mathrm{X} \). The graph is a straight line through the origin.
What is the slope of the graph?
ⓐ. \(+1\)
ⓑ. \(+2\)
ⓒ. \(-1\)
ⓓ. \(-2\)
Correct Answer: \(+2\)
Explanation: \( \textbf{Formula family:} \) The neutral compound is \( \mathrm{XO_n} \).
\( \textbf{Oxygen contribution:} \) Each oxygen is \(-2\), so \(n\) oxygen atoms contribute \(-2n\).
\( \textbf{Neutrality condition:} \)
\[
x+(-2n)=0
\]
\[
x=+2n
\]
\( \textbf{Graph meaning:} \) The y-axis value is \(x\), and the x-axis value is \(n\).
\[
\frac{x}{n}=+2
\]
\( \textbf{Final answer:} \) The slope is \(+2\). Each additional ordinary oxygen atom raises the required oxidation number of \( \mathrm{X} \) by \(2\) units in this neutral formula pattern.
111. In the neutral compound \( \mathrm{H_2S} \), the oxidation number of sulphur is:
ⓐ. \(-2\)
ⓑ. \(-1\)
ⓒ. \(+1\)
ⓓ. \(+2\)
Correct Answer: \(-2\)
Explanation: \( \textbf{Known value:} \) Hydrogen is \(+1\) when bonded to a non-metal.
\( \textbf{Hydrogen contribution:} \)
\[
2(+1)=+2
\]
\( \textbf{Neutral compound condition:} \) The total must be \(0\).
\( \textbf{Let sulphur be } x: \)
\[
2+x=0
\]
\[
x=-2
\]
\( \textbf{Final answer:} \) Sulphur is \(-2\) in \( \mathrm{H_2S} \). The subscript on hydrogen affects the total hydrogen contribution, not the oxidation number assigned to one hydrogen atom.
112. For \( \mathrm{CO_2} \), the oxidation number of carbon is:
ⓐ. \(+4\)
ⓑ. \(-4\)
ⓒ. \(+2\)
ⓓ. \(+6\)
Correct Answer: \(+4\)
Explanation: \( \textbf{Known value:} \) Oxygen is \(-2\) in ordinary \( \mathrm{CO_2} \).
\( \textbf{Oxygen contribution:} \)
\[
2(-2)=-4
\]
\( \textbf{Neutral molecule rule:} \) The sum of oxidation numbers must be \(0\).
\( \textbf{Let carbon be } x: \)
\[
x-4=0
\]
\[
x=+4
\]
\( \textbf{Final answer:} \) Carbon has oxidation number \(+4\) in \( \mathrm{CO_2} \). The formula contains two oxygen atoms, so the oxygen contribution is \(-4\), not only \(-2\).
113. In \( \mathrm{NH_3} \), using \( \mathrm{H}=+1 \), the oxidation number of nitrogen is:
ⓐ. \(0\)
ⓑ. \(+3\)
ⓒ. \(+5\)
ⓓ. \(-3\)
Correct Answer: \(-3\)
Explanation: \( \textbf{Known value:} \) Hydrogen is \(+1\) in \( \mathrm{NH_3} \).
\( \textbf{Hydrogen contribution:} \)
\[
3(+1)=+3
\]
\( \textbf{Neutral molecule rule:} \)
\[
x+3=0
\]
\( \textbf{Solve for nitrogen:} \)
\[
x=-3
\]
\( \textbf{Final answer:} \) Nitrogen is \(-3\) in \( \mathrm{NH_3} \). The negative value means nitrogen is assigned the electron share more strongly than hydrogen in this formal oxidation-number method.
114. A data record gives two iron oxides:
| Compound | Oxidation number of oxygen | Oxidation number of iron |
|---|
| \( \mathrm{FeO} \) | \(-2\) | ? |
| \( \mathrm{Fe_2O_3} \) | \(-2\) | ? |
The oxidation numbers of iron in \( \mathrm{FeO} \) and \( \mathrm{Fe_2O_3} \), respectively, are:
ⓐ. \(+1\) and \(+2\)
ⓑ. \(+3\) and \(+2\)
ⓒ. \(+2\) and \(+6\)
ⓓ. \(+2\) and \(+3\)
Correct Answer: \(+2\) and \(+3\)
Explanation: \( \textbf{For } \mathrm{FeO}: \) Oxygen is \(-2\), and the compound is neutral.
\[
x+(-2)=0
\]
\[
x=+2
\]
\( \textbf{For } \mathrm{Fe_2O_3}: \) Three oxygen atoms contribute \(3(-2)=-6\).
\[
2x-6=0
\]
\[
2x=6
\]
\[
x=+3
\]
\( \textbf{Final answer:} \) Iron is \(+2\) in \( \mathrm{FeO} \) and \(+3\) in \( \mathrm{Fe_2O_3} \). The subscript \(2\) on iron in \( \mathrm{Fe_2O_3} \) divides the total iron contribution between two iron atoms.
115. A learner calculates the oxidation number of iron in \( \mathrm{Fe_2O_3} \) as \(+6\) by writing \(x+3(-2)=0\). The correction is:
ⓐ. use \(x+3(-2)=-3\), because oxygen has charge \(-3\)
ⓑ. use \(2x+3(-2)=0\), because there are two iron atoms
ⓒ. use \(x+2(-2)=0\), because the subscript on iron multiplies oxygen
ⓓ. use \(x=0\), because iron is a metal
Correct Answer: use \(2x+3(-2)=0\), because there are two iron atoms
Explanation: The formula \( \mathrm{Fe_2O_3} \) contains two iron atoms and three oxygen atoms. If each iron has oxidation number \(x\), the total iron contribution is \(2x\), not \(x\). Oxygen contributes \(3(-2)=-6\). The neutral compound condition gives \(2x-6=0\), so \(x=+3\). The value \(+6\) is the total contribution of both iron atoms, not the oxidation number of one iron atom.
116. The pair with the same oxidation number of the central atom is:
ⓐ. \( \mathrm{NO_2} \) and \( \mathrm{N_2O_4} \)
ⓑ. \( \mathrm{CO_2} \) and \( \mathrm{CO} \)
ⓒ. \( \mathrm{SO_2} \) and \( \mathrm{SO_3} \)
ⓓ. \( \mathrm{FeO} \) and \( \mathrm{Fe_2O_3} \)
Correct Answer: \( \mathrm{NO_2} \) and \( \mathrm{N_2O_4} \)
Explanation: \( \textbf{For } \mathrm{NO_2}: \)
\[
x+2(-2)=0
\]
\[
x=+4
\]
\( \textbf{For } \mathrm{N_2O_4}: \)
\[
2x+4(-2)=0
\]
\[
2x=8
\]
\[
x=+4
\]
\( \textbf{Comparison:} \) Nitrogen is \(+4\) in both formulas.
\( \textbf{Other pairs:} \) Carbon is \(+4\) in \( \mathrm{CO_2} \) but \(+2\) in \( \mathrm{CO} \); sulphur is \(+4\) in \( \mathrm{SO_2} \) but \(+6\) in \( \mathrm{SO_3} \); iron is \(+2\) in \( \mathrm{FeO} \) but \(+3\) in \( \mathrm{Fe_2O_3} \).
\( \textbf{Final answer:} \) \( \mathrm{NO_2} \) and \( \mathrm{N_2O_4} \) have the same average oxidation number of nitrogen. Doubling a formula does not necessarily change the oxidation number.
117. In the set \( \mathrm{CO} \), \( \mathrm{CO_2} \), and \( \mathrm{CH_4} \), the oxidation numbers of carbon are respectively:
ⓐ. \(+4, +2, -4\)
ⓑ. \(-2, -4, +4\)
ⓒ. \(+2, +4, -4\)
ⓓ. \(0, +4, +4\)
Correct Answer: \(+2, +4, -4\)
Explanation: \( \textbf{For } \mathrm{CO}: \) Oxygen is \(-2\), so \(x-2=0\), giving carbon \(+2\).
\( \textbf{For } \mathrm{CO_2}: \) Two oxygen atoms contribute \(-4\), so carbon is \(+4\).
\( \textbf{For } \mathrm{CH_4}: \) Hydrogen is \(+1\), so \(x+4(+1)=0\).
\[
x+4=0
\]
\[
x=-4
\]
\( \textbf{Final answer:} \) The sequence is \(+2, +4, -4\). Carbon can show both positive and negative oxidation numbers depending on the element bonded to it.
118. In \( \mathrm{H_2O} \), the oxidation numbers of hydrogen and oxygen are:
ⓐ. \( \mathrm{H}=-1 \), \( \mathrm{O}=+2 \)
ⓑ. \( \mathrm{H}=+1 \), \( \mathrm{O}=-2 \)
ⓒ. \( \mathrm{H}=0 \), \( \mathrm{O}=0 \)
ⓓ. \( \mathrm{H}=+2 \), \( \mathrm{O}=-1 \)
Correct Answer: \( \mathrm{H}=+1 \), \( \mathrm{O}=-2 \)
Explanation: Water is a neutral compound, and hydrogen is usually \(+1\) when bonded to oxygen. Two hydrogen atoms therefore contribute \(2(+1)=+2\). Oxygen must contribute \(-2\) so that the total is \(0\). This agrees with the ordinary oxygen rule in most compounds. Water is not a metal hydride or peroxide, so the special exception values are not used.
119. A compact oxidation-number comparison gives \( \mathrm{H_2O} \), \( \mathrm{H_2O_2} \), and \( \mathrm{O_2} \). The oxidation numbers of oxygen are respectively:
ⓐ. \(-1, -2, 0\)
ⓑ. \(0, -1, -2\)
ⓒ. \(-2, 0, -1\)
ⓓ. \(-2, -1, 0\)
Correct Answer: \(-2, -1, 0\)
Explanation: In \( \mathrm{H_2O} \), oxygen has its usual oxidation number \(-2\). In \( \mathrm{H_2O_2} \), the compound is a peroxide, so oxygen is \(-1\). In \( \mathrm{O_2} \), oxygen is in its elemental form, so its oxidation number is \(0\). The same element can have different oxidation numbers in different chemical forms. Recognising the compound class is more reliable than applying one oxygen value mechanically.
120. The oxidation number of sulphur in \( \mathrm{H_2SO_4} \) is:
ⓐ. \(+2\)
ⓑ. \(+4\)
ⓒ. \(+6\)
ⓓ. \(+8\)
Correct Answer: \(+6\)
Explanation: \( \textbf{Known values:} \) Hydrogen is \(+1\), and oxygen is \(-2\).
\( \textbf{Hydrogen contribution:} \)
\[
2(+1)=+2
\]
\( \textbf{Oxygen contribution:} \)
\[
4(-2)=-8
\]
\( \textbf{Neutral molecule condition:} \) The total must be \(0\).
\( \textbf{Let sulphur be } x: \)
\[
2+x-8=0
\]
\[
x=+6
\]
\( \textbf{Final answer:} \) Sulphur is \(+6\) in \( \mathrm{H_2SO_4} \). Both hydrogen atoms and all four oxygen atoms must be counted in the algebra.
