Live practice

Lead(II) oxide loses oxygen and forms lead, so lead(II) oxide is reduced. Carbon gains oxygen and forms carbon dioxide, so carbon is oxidised.

Therefore statements (c) and (d) are correct. Statements (a) and (b) are incorrect: it is lead oxide that is reduced, and carbon dioxide is the product of oxidation rather than the substance being oxidised.

Assume, contrary to what is required, that \(3+2\sqrt5\) is rational. Let

Rearranging,

Since rational numbers are closed under subtraction and division by a non-zero rational number, \((r-3)/2\) is rational. This would make \(\sqrt5\) rational.

But \(\sqrt5\) is irrational. This contradiction shows that \(3+2\sqrt5\) is irrational.

Aluminium is more reactive than iron and displaces iron from iron(III) oxide. Thus one element replaces another element in its compound.

The reaction is therefore a displacement reaction. It is also the thermite redox reaction.

(i) \(\dfrac{1}{\sqrt2}\)

Assume that \(1/\sqrt2\) is rational. Let \(1/\sqrt2=r\), where \(r\in\mathbb Q\). Since \(r\ne0\),

The reciprocal of a non-zero rational number is rational, so this would make \(\sqrt2\) rational, a contradiction. Hence \(1/\sqrt2\) is irrational.

(ii) \(7\sqrt5\)

Assume that \(7\sqrt5=r\), where \(r\in\mathbb Q\). Then

Since \(\frac{r}{7}\) is rational, this contradicts the irrationality of \(\sqrt5\). Hence \(7\sqrt5\) is irrational.

(iii) \(6+\sqrt2\)

Assume that \(6+\sqrt2=r\), where \(r\in\mathbb Q\). Then

Since \(r-6\) is rational, this contradicts the irrationality of \(\sqrt2\). Hence \(6+\sqrt2\) is irrational.

Iron is more reactive than hydrogen. It displaces hydrogen from dilute hydrochloric acid and forms iron(II) chloride:

Hence hydrogen gas and iron chloride are produced.

A balanced chemical equation contains an equal number of atoms of each element on the reactant side and the product side.

During a chemical reaction, atoms are rearranged; they are neither created nor destroyed. Therefore, the total mass of the reactants must equal the total mass of the products. Chemical equations are balanced to satisfy this law of conservation of mass.

(a) Balance nitrogen first and then hydrogen:

(b) Two molecules of hydrogen sulphide give two sulphur dioxide molecules and two water molecules:

(c) Three barium ions are required for the three sulphate ions:

(d) Balance potassium and water with coefficient 2; hydrogen is released:

(a) Two nitrate ions are present in calcium nitrate, so place 2 before nitric acid. Hydrogen and oxygen then require 2 water molecules:

(b) Two sodium atoms are required for sodium sulphate:

(c) The equation already has one atom or ion group of each kind on both sides:

(d) Two chloride ions on the left require 2 molecules of HCl on the right:

(a)

(b) Zinc nitrate contains two nitrate ions, so place 2 before silver nitrate and silver:

(c) The least common multiple of 2 chlorine atoms in \(\ce{CuCl2}\) and 3 in \(\ce{AlCl3}\) is 6:

(d) Two potassium and two chlorine atoms are balanced by placing 2 before KCl:

(a)

The ions exchange partners; this is a double displacement reaction.

(b)

One compound breaks into simpler products; this is a decomposition reaction.

(c)

Two reactants form one product; this is a combination reaction.

(d)

Magnesium displaces hydrogen; this is a displacement reaction.