Mixed Problems: Set 3 (Metals and the f-Block)

Transcript

0:00Introduction

Hello everyone! Let us start with a one-minute question. Drop a piece of zinc into sodium hydroxide, a strong base. Metals dissolve in acids, not in bases, so nothing happens, right? Hmm, hold that thought; Example two will settle it. This is Set three of the mixed problems on the d and f blocks: the metals, and the f block, that is, the lanthanoids and the actinoids. Questions of this kind appear in JEE Main, and each one should take you about a minute. So, let's begin.

0:34Lanthanoid ions: the +3 state

First, the f block, starting with the lanthanoids, from cerium to lutetium. L n is the short symbol for any lanthanoid, and the raised three plus is its charge. Every L n three plus ion has the xenon core, the X e in square brackets, and then some electrons in the four f subshell; the small raised letter n counts them. Okay? So, lanthanum three plus is four f zero, cerium three plus is four f one, and so on, up to lutetium three plus, which is four f fourteen. The three dots stand for the ions in between, and the raised number counts the four f electrons. Right? Now the oxidation states. Plus three is the characteristic state of the lanthanoids. Plus two or plus four appear when they give an empty, a half-filled or a completely filled f set: f zero, f seven or f fourteen. Clear? Now a quick one from this set. Which L n three plus ion has a half-filled four f subshell? Gadolinium three plus, yes, exactly! The four f subshell holds fourteen electrons, so half-filled means four f seven. In the plus three state, that is gadolinium. Got it?

1:42The lanthanoid contraction

Next, the lanthanoid contraction. From lanthanum to lutetium, the atomic and ionic radii fall steadily. Lanthanum three plus is about one hundred and six picometres, and lutetium three plus is about eighty five picometres. The wavy equals sign means about, and p m means picometres. With me? Now the cause. Each new electron enters the four f subshell, and four f electrons shield one another poorly from the nucleus, because f orbitals are so diffuse. So the effective nuclear charge rises, and the size shrinks. Okay? Here is the next one from this set. Lanthanum hydroxide, gadolinium hydroxide and lutetium hydroxide; the O H in brackets with the small three below means three hydroxide groups. Lutetium is the heaviest of the three, so its hydroxide is the most basic, right? No, no, careful, it goes the other way! Because of the contraction, the L n three plus ion gets smaller from lanthanum to lutetium, and its compounds become more covalent. So the basicity of the hydroxides falls from lanthanum to lutetium. Right? So the most basic is lanthanum hydroxide, at the start of the series.

2:56Actinoids: many oxidation states

Clear? Now the actinoids, from thorium to lawrencium. Their configuration is the radon core, R n in square brackets, then five f, zero to fourteen, six d, zero to one, and seven s two; each small dash means from the first number to the second. Plutonium, P u, is five f six, then seven s two. Got it? The key point: the five f, six d and seven s levels are close in energy. And five f orbitals are less buried than four f orbitals, so five f electrons join in bonding. Okay? So, a quick one from this set. What is the highest oxidation state shown by plutonium? Just plus three, like the lanthanoids? No, it goes much higher than that! Plus three is common for the actinoids, but the early actinoids use their five f, six d and seven s electrons. So neptunium and plutonium go up to plus seven, and that is the answer.

3:54Metals: ores, slag and refining

Right? Now the metals, and first, the ores. Calamine is an ore of zinc. What is its formula? Zinc carbonate, yes, exactly! Calamine is a carbonate ore of zinc, Z n C O three; the small three written low means three oxygen atoms. Okay? Next, the blast furnace, where iron is extracted. Limestone gives calcium oxide, C a O on screen, and that calcium oxide removes the silica. Right? So let me ask you this: what is the slag in the blast furnace? Calcium silicate, very good! Calcium oxide plus S i O two, which is silica, gives C a S i O three, calcium silicate; the arrow means gives. Clear? And last, refining. In the Mond process, nickel combines with carbon monoxide to form N i, C O in brackets, four, which is nickel carbonyl, and it is volatile. The carbonyl vapour is then heated more strongly, and it decomposes to give pure nickel. With me?

4:57Example 1: spin-only magnetic moment of Ce3+

Now, Example one, an easy one from this set. Find the spin-only magnetic moment of cerium three plus. Pause the video and try it first. Done? Okay, let's check. Mu, the Greek letter on screen, is the spin-only moment. Mu equals the square root of n, times n plus two, in B M, which stands for Bohr magnetons; the tick shaped sign is the square root. And n is the number of unpaired electrons, not the total. Okay? Cerium is the xenon core, then four f one, five d one, six s two. For cerium three plus, three electrons must go. Right? Many students remove the two six s electrons, and then the four f electron. That leaves four f zero, so the moment is zero, right? No, no, wait, that is the trap! Cerium three plus loses the two six s electrons and the five d electron, and the four f electron stays. So it is four f one, with one unpaired electron, so n equals one. Clear? So mu is the square root of one times three, the cross meaning times, which is root three. That is about one point seven three Bohr magnetons. Got it?

6:14Example 2: volume of H2 at STP from 6.54 g Zn in NaOH

Now Example two, a step harder, and it settles our opening question. What volume of hydrogen, at STP, is released when six point five four grams of zinc dissolves in excess sodium hydroxide? STP means standard temperature and pressure, and g means grams. Pause the video and try it first. Done? Okay, let's check. First, our opening question. Sodium hydroxide is a base. Does zinc react with it at all? Yes, it does, because zinc is amphoteric: it reacts with acids and with bases. Z n plus two N a O H gives N a two Z n O two, sodium zincate, plus H two, hydrogen gas. Okay? Now the moles of zinc. The molar mass of zinc is sixty five point four grams per mole; the raised minus one means per. So six point five four over sixty five point four gives zero point one mole. Right? Look at the equation: one mole of zinc gives one mole of hydrogen. So zero point one mole of zinc gives zero point one mole of hydrogen. With me? At STP, one mole of a gas occupies twenty two point four litres, and capital L means litres. So zero point one times twenty two point four gives two point two four litres. And our opening puzzle is solved: zinc does dissolve in a base, and it gives off hydrogen. Got it?

7:42Quick revision: Gd3+, Ln(OH)3 basicity, Pu +7, ores, slag

So, quick revision. First, the lanthanoids: gadolinium three plus is four f seven, half-filled, and the lanthanoid contraction makes the hydroxides less basic from lanthanum to lutetium. Second, the actinoids use their five f, six d and seven s electrons, so neptunium and plutonium reach plus seven. Third, the metals: calamine is zinc carbonate, the blast furnace slag is calcium silicate, the Mond process refines nickel, and zinc is amphoteric. Now open Set three, give each problem about a minute, then try the practice problem at the end. All the best!