Live practice

(i) The substance used to prepare the whitewashing solution is quicklime, or calcium oxide. Its formula is \(\ce{CaO}\).

(ii) Calcium oxide combines vigorously with water to form calcium hydroxide (slaked lime), releasing heat:

The solution of calcium hydroxide is applied to walls for whitewashing.

For two positive integers \(a\) and \(b\),

Therefore,

Hence, \(\operatorname{LCM}(306,657)=22338\).

On passing electric current through acidified water, water decomposes into hydrogen and oxygen:

The balanced equation shows that two volumes of hydrogen are formed for every one volume of oxygen. Therefore, the gas collected in double the amount is hydrogen. It is collected at the cathode, while oxygen is collected at the anode.

If \(6^n\) ended with the digit \(0\), it would be divisible by \(10=2\times5\). Its prime factorisation would therefore contain both \(2\) and \(5\).

However,

By the uniqueness of prime factorisation, the only prime factors of \(6^n\) are \(2\) and \(3\); it has no factor \(5\).

Therefore, \(6^n\) cannot end with the digit \(0\) for any natural number \(n\).

Iron is more reactive than copper, so it displaces copper from copper sulphate solution:

The blue copper sulphate solution is converted into pale-green iron(II) sulphate solution. Copper is deposited as a reddish-brown coating on the nail. Hence the colour of the solution changes.

For the first number, take \(13\) as a common factor:

It is a product of two integers greater than \(1\), so it is composite.

For the second number, take \(5\) as a common factor:

It is also a product of two integers greater than \(1\), so it is composite.

When aqueous lead(II) nitrate and potassium iodide are mixed, their ions exchange partners. Insoluble lead(II) iodide forms as a yellow precipitate:

Since the cations and anions of the two reactants are exchanged, this is a double displacement reaction.

They will be together at the starting point after a time that is a common multiple of \(18\) minutes and \(12\) minutes. The least such time is their LCM.

Therefore, Sonia and Ravi will meet again at the starting point after 36 minutes.

(i) Sodium gains oxygen to form sodium oxide; therefore sodium is oxidised. Oxygen combines with sodium and is reduced.

(ii) Hydrogen gains oxygen to form water, so hydrogen is oxidised. Copper(II) oxide loses oxygen to form copper, so copper(II) oxide is reduced.

Assume, contrary to what is required, that \(\sqrt5\) is rational. Then it can be written in lowest terms as

Squaring both sides gives

Thus \(5\mid a^2\). Since \(5\) is prime, \(5\mid a\). Let \(a=5k\) for some integer \(k\). Substitution gives

Hence \(5\mid b^2\), and therefore \(5\mid b\). Thus \(5\) is a common factor of \(a\) and \(b\), contradicting \(\gcd(a,b)=1\).

Therefore, the assumption is false and \(\sqrt5\) is irrational.