ESAT Paper 4 Chemistry Sample Questions

Correct Answer: D. 3978

Step-by-Step Breakdown:

1. Total the electrons

The atom is neutral, so it holds one electron for every proton: $12$ electrons. Each one is $\frac{1}{1836}$ on the relative mass scale, so together they come to

2. Divide the nuclear mass by that total

Every nucleon has relative mass $1$, so the nucleus of $^{26}_{12}\mathrm{Mg}$ weighs its mass number: $12$ protons and $14$ neutrons give $12 + 14 = 26$. Dividing by a fraction means multiplying by its reciprocal:

Sanity check by a second route: one nucleon outweighs one electron by $1836$, and there are $26$ nucleons against $12$ electrons, so the factor is $1836 \times \frac{26}{12} = 3978$. The two routes agree, and a factor of several thousand is exactly what the claim that almost all of an atom's mass sits in its nucleus amounts to numerically.

The key is $3978$.

Why the Other Options Are Wrong (❌):

• A. 153 · Intermediate value quoted
  Stops one line early. The working $\frac{12}{1836} = \frac{1}{153}$ gives the electrons' combined relative mass, and the $153$ sitting in that fraction is quoted as the answer. It is only a denominator, and the nuclear mass of $26$ has not been used at all.
• B. 2142 · Protons omitted from the nucleus
  Counts only the $14$ neutrons as the mass of the nucleus, forgetting that each of the $12$ protons also carries relative mass $1$, and computes $14 \times 153 = 2142$ in place of $26 \times 153$.
• C. 47736 · One electron instead of all
  Compares the whole nucleus with a single electron: $26 \times 1836 = 47736$. The figure $1836$ is the factor for one electron only, so this overshoots by a factor of $12$, the number of electrons the neutral atom actually has.
• E. 5814 · Mass number read as the neutron count
  Reads the mass number as neutrons alone and then adds the protons on top, making the nucleus $26 + 12 = 38$ nucleons and giving $38 \times 153 = 5814$. The mass number $26$ already counts the $12$ protons, so adding them a second time counts them twice.
• F. 26 · Nucleus compared with one nucleon
  Compares the nucleus with a single particle of relative mass $1$ rather than with the electrons, which hands back the mass number itself: $26$. The comparison asked for is against all $12$ electrons of the neutral atom together, and their combined relative mass is $\frac{12}{1836} = \frac{1}{153}$, not $1$. Dividing by that fraction multiplies by $153$, so the factor is $26 \times 153 = 3978$.
• G. 572832 · Reciprocal formed by multiplying instead of flipping
  Divides by $\frac{12}{1836}$ by multiplying by $1836 \times 12$: $1836 \times 26 \times 12$. Flipping a fraction sends the $12$ underneath rather than leaving it on top, so the multiplier is $\frac{1836}{12} = 153$ and the factor is $26 \times 153 = 3978$, which this option exceeds by a factor of $12^2$.

Common Mistake (⚠️):
Comparing the nucleus with a single electron rather than with all of them. The value $\frac{1}{1836}$ belongs to one electron, so it has to be multiplied by the $12$ electrons a neutral atom of magnesium carries before the division is done, and skipping that step inflates the answer by a factor of $12$.

Takeaway (📌):
The whole item is $1836$ times the mass number over the proton number, because a neutral atom's electron count is its proton count. Cancel $1836$ against $12$ before you multiply and what is left is one short product.

Correct Answer: A. 31

Step-by-Step Breakdown:

1. Turn the electron count into the atomic number

Charge is the count of electrons missing or spare. This ion has gained three electrons relative to the neutral atom, so it carries three electrons more than protons:

$Z = 18 - 3 = 15$

That proton count is the atomic number, the figure written at the bottom left.

2. Add the neutrons to reach the mass number

The mass number totals protons and neutrons and nothing else, because an electron is far too light to register in it:

$A = Z + n = 15 + 16 = 31$

Sanity check: read the notation back. From $^{31}_{15}\mathrm{X}$ the neutrons are $31 - 15 = 16$, and an ion of charge $3-$ built on $15$ protons holds $15 + 3 = 18$ electrons. Both match what was measured.

The key is $31$.

Why the Other Options Are Wrong (❌):

• B. 16 · Neutron count read as the mass number
  Stops at the neutrons. The mass number counts protons and neutrons together, so $16$ omits every one of the $15$ protons; neutrons are never printed on their own in $^{A}_{Z}\mathrm{X}$: they are only ever the difference $A - Z$.
• C. 34 · Ion treated as a neutral atom
  Reads the $18$ electrons straight off as the proton count, which is true only of a neutral atom. This ion has gained three electrons, so the protons come to $18 - 3 = 15$ and the mass number to $15 + 16 = 31$.
• D. 37 · Charge applied in the wrong direction
  Moves the electron count the wrong way. This $3-$ ion has gained three electrons, so it holds three electrons more than protons and the proton count is $18 - 3 = 15$, not $21$.
• E. 49 · Electrons counted into the mass number
  Adds the $18$ electrons to the nucleons as well. An electron is far too light to register in a mass number, which totals the $15$ protons and the $16$ neutrons and nothing else.
• F. 28 · Charge applied a second time
  Uses the charge twice. It turns the electron count into the proton count once, $18 - 3 = 15$, and this option applies the same correction again to the finished total: $31 - 3$. A mass number counts the $15$ protons and the $16$ neutrons and nothing else, so once the charge has delivered the protons its work is done and $A = 15 + 16 = 31$.

Common Mistake (⚠️):
Treating the ion as though it were neutral. Only in a neutral atom does the electron count double as the proton count; this ion has gained three electrons, so its $18$ electrons and its $15$ protons differ by $3$, and using $18$ as the atomic number shifts the mass number by that same $3$.

Takeaway (📌):
Charge first, then add. The charge turns the electron count into the proton count, $18 - 3 = 15$, and the mass number is that proton count plus the neutrons. Electrons never enter a mass number at all.

Correct Answer: F. 0.36

Step-by-Step Breakdown:

1. Recover the total volume of hydrogen

A mean rate is the total change divided by the time it took, so the total is the rate multiplied by the interval. Only the hydrogen reaches the syringe, so its reading follows that one substance:

2. Convert to moles of hydrogen, then to moles of ethanoic acid

The balanced equation pairs $2\,\mathrm{CH_3COOH}$ with $1\,\mathrm{H_2}$, so the amount of ethanoic acid is $\tfrac{2}{1}$ times the amount of hydrogen:

3. Convert the amount to a mass

Check the units before committing. Dividing $72\,\mathrm{cm^3}$ by a molar volume quoted in $\mathrm{dm^3}$ would have given $3\,\mathrm{mol}$ of hydrogen and a final mass of $360\,\mathrm{g}$, which a syringe holding $72\,\mathrm{cm^3}$ cannot account for.

The key is $0.36$.

Why the Other Options Are Wrong (❌):

• A. 0.006 · Amount in moles reported as a mass
  The amount in moles was written down as though it were already a mass: $n(\mathrm{CH_3COOH})=0.006\,\mathrm{mol}$ was quoted as $0.006\,\mathrm{g}$. The last conversion is still owed, and it is the one the stem hands over: multiplying by $M_r(\mathrm{CH_3COOH})=60$ gives $0.36$.
• B. 0.18 · Stoichiometric ratio ignored
  The equation's coefficients were skipped and the amount of ethanoic acid was set equal to the amount of hydrogen, $0.003\,\mathrm{mol}$ rather than $0.006\,\mathrm{mol}$, before multiplying by $60$. The equation pairs $2\,\mathrm{CH_3COOH}$ with $1\,\mathrm{H_2}$, so the amount of ethanoic acid is $\tfrac{2}{1}$ times the amount of hydrogen, and this option is the key $0.36$ scaled by $\tfrac{1}{2}$.
• C. 0.852 · Wrong relative formula mass used
  The right amount, $0.006\,\mathrm{mol}$, was multiplied by the relative formula mass of magnesium ethanoate instead: $142$ rather than the $60$ the stem supplies. $M_r((\mathrm{CH_3COO})_2\mathrm{Mg})=142$ is genuine, but it belongs to another substance in the equation, and the question asks for the mass of ethanoic acid.
• D. 360 · Molar volume units mismatched
  The volume was left in $\mathrm{cm^3}$ and divided by a molar volume quoted in $\mathrm{dm^3}$: $72\div24=3\,\mathrm{mol}$ of hydrogen instead of $0.003\,\mathrm{mol}$. One mole of gas occupies $24\,\mathrm{dm^3}$, which is $24000\,\mathrm{cm^3}$, so this option is the key $0.36$ multiplied by a thousand.
• E. 0.09 · Mole ratio turned upside down
  The equation's coefficients were read the wrong way up. The $0.003\,\mathrm{mol}$ of hydrogen was scaled by $\tfrac{1}{2}$ instead of $\tfrac{2}{1}$ before the relative formula mass was applied, so this option is the key $0.36$ divided by $\left(\tfrac{2}{1}\right)^2$. The equation pairs $2\,\mathrm{CH_3COOH}$ with $1\,\mathrm{H_2}$, and it is the ethanoic acid that is being counted, so the amount wanted is $0.006\,\mathrm{mol}$ and the mass is $0.36$.
• G. 8.64 · Molar volume never divided in
  The volume was converted to $\mathrm{dm^3}$ and then treated as though it were already an amount: $0.072$ went straight into the $2$ to $1$ scaling and then into the multiplication by $60$, with no division by the molar volume anywhere. A volume becomes an amount only by dividing by $24\,\mathrm{dm^3\,mol^{-1}}$, which turns $0.072\,\mathrm{dm^3}$ into $0.003\,\mathrm{mol}$, so this option is the key $0.36$ multiplied by $24$.
• H. 0.72 · Equation coefficient counted a second time
  The $2$ to $1$ from the equation was used twice: once correctly, turning $0.003\,\mathrm{mol}$ of hydrogen into $0.006\,\mathrm{mol}$ of ethanoic acid, and again at the mass step, as though the coefficient scaled the relative formula mass as well. It does not: $M_r(\mathrm{CH_3COOH})=60$ means one mole of ethanoic acid has a mass of $60\,\mathrm{g}$ whatever the equation's coefficients are, so the mass is $0.006\times60=0.36$ and the ratio is spent once.

Common Mistake (⚠️):
Starting the mole calculation from the rate itself. A figure in $\mathrm{cm^3\,s^{-1}}$ is not a volume, so it has to be multiplied by the $90\,\mathrm{s}$ interval before the molar gas volume can be used; feeding $0.8$ straight into the division gives an amount $90$ times too small.

Takeaway (📌):
Rate times time gives the volume of hydrogen; the molar gas volume, the $2$ to $1$ from the balanced equation and $M_r(\mathrm{CH_3COOH})=60$ then run the chain backwards to the ethanoic acid. Following a product is only ever a way of following the reactant that made it.

Correct Answer: G. 12

Step-by-Step Breakdown:

1. Find the amount of nickel displaced

The manganese is in excess, so every nickel ion reacts and the nickel(II) sulfate is the limiting reagent. The volume in cubic decimetres is $0.1\ \text{dm}^3$, so

The reaction is $\mathrm{Mn} + \mathrm{Ni^{2+}} \rightarrow \mathrm{Mn^{2+}} + \mathrm{Ni}$, one nickel atom for each nickel ion, so $0.03\ \text{mol}$ of nickel is displaced.

2. Convert that amount into a total heat

3. Turn the heat into a temperature rise

What warms up is the $100\ \text{cm}^3$ of solution, and at a density of $1\ \text{g cm}^{-3}$ that is $100\ \text{g}$. The metal's mass is ignored and the cup loses no heat, so all $5040\ \text{J}$ goes into the solution. Rearranging $Q = mc\Delta T$,

Sanity check: $420\ \text{J}$ raises this solution by one degree, and $5040$ is $12$ times $420$, so $12$ degrees. Notice that the volume never reaches the answer: it fixes the amount reacting and the mass warmed in the same proportion, so it cancels, and the rise depends only on the concentration, the energy per mole, the density and the specific heat capacity.

The temperature rise is $12\ ^\circ\text{C}$.

Why the Other Options Are Wrong (❌):

• A. 1.2 · Volume conversion off by ten
  The volume was divided by $10000$ instead of $1000$, $100\ \text{cm}^3$ taken as $0.01\ \text{dm}^3$, giving $n = 0.003\ \text{mol}$ and $Q = 0.504\ \text{kJ}$, then $504 \div 420 = 1.2$. A $\text{dm}^3$ is a thousand $\text{cm}^3$, so the volume is $0.1\ \text{dm}^3$ and the amount reacting is ten times larger than this.
• B. 6 · Ionic charge used as a mole ratio
  The $2+$ charge on the nickel ion was used as a stoichiometric factor and the amount divided by $2$ to $0.015\ \text{mol}$: $0.015 \times 168 = 2.52\ \text{kJ}$ and $2520 \div 420 = 6$. The charge counts the electrons transferred, not the atoms: each nickel ion gives one nickel atom, so the amount stays at $0.03\ \text{mol}$.
• C. 50.4 · Specific heat capacity omitted
  The specific heat capacity was dropped from the denominator: $5040 \div 100 = 50.4$. Dividing joules by a mass alone leaves $\text{J g}^{-1}$, an energy per gram and not a temperature at all; it is the $4.2$ that turns joules per gram into degrees.
• D. 400 · Scaling by the amount omitted
  The per-mole figure was treated as the total heat released: $168\ \text{kJ} = 168000\ \text{J}$ and $168000 \div 420 = 400$. Only $0.03\ \text{mol}$ of nickel is displaced, so only that fraction of the $168\ \text{kJ}$ is ever given out, and $400$ is the rise a whole mole would produce.
• E. 0.012 · Kilojoules divided by a joules-per-degree
  The amount and the heat are both right, $0.03\ \text{mol}$ giving $5.04\ \text{kJ}$, but that heat was divided by $420$ while still in kilojoules. A specific heat capacity of $4.2\ \text{J g}^{-1}\,^\circ\text{C}^{-1}$ prices a degree in JOULES, so the heat has to be rewritten as $5040\ \text{J}$ before it meets $420$, and $5040 \div 420 = 12$, a thousand times this.
• F. 120 · Concentration read off as the amount
  A concentration is a count of moles per cubic decimetre, not a count of moles. Taking $0.3\ \text{mol dm}^{-3}$ as $0.3\ \text{mol}$ of nickel leaves the volume out of the amount reacting, and the rise then comes out as $12 \div 0.1$. Only $0.1\ \text{dm}^3$ was poured, so the amount is $0.3 \times 0.1 = 0.03\ \text{mol}$ and the rise is $12\ ^\circ\text{C}$.
• H. 5.04 · The heat reported instead of the rise
  This is where the calculation stands after two steps and not at the end: $0.03 \times 168 = 5.04\ \text{kJ}$ is the heat the displacement gives out, in kilojoules, and the question asks how much warmer the solution gets, in $^\circ\text{C}$. Warming $100\ \text{g}$ of solution by one degree costs $100 \times 4.2 = 420\ \text{J}$, so $5040\ \text{J}$ buys $12\ ^\circ\text{C}$.

Common Mistake (⚠️):
Dividing the heat by the amount instead of multiplying, out of habit from the more familiar calorimetry question that asks for kilojoules per mole. Here the energy per mole is handed over, $168\ \text{kJ}$, and the temperature rise is what is wanted, so the amount $0.03\ \text{mol}$ multiplies up to a total heat of $5040\ \text{J}$ first, and only then does $Q = mc\Delta T$ get rearranged.

Takeaway (📌):
Work out what one degree costs before anything else. The product $mc$ is the price of a degree in joules, here $420\ \text{J}$, and every calorimetry question that supplies the mass and the specific heat capacity is then either a heat divided by that price or that price multiplied by a rise.

Correct Answer: D. 40

Step-by-Step Breakdown:

1. Read the two numbers off the label, then take the difference

The label gives the nuclide as $^{72}_{32}\mathrm{Ge}$. The lower figure is the atomic number, $Z = 32$, and it counts protons only: it is what makes the sample germanium rather than anything else. The upper figure is the mass number, $A = 72$, and it counts protons and neutrons together, because the electrons are far too light to register in it. Neutrons appear in $A$ and nowhere else on the label, so removing the protons from the mass number leaves them:

$n = A - Z = 72 - 32 = 40$

Sanity check: the neutron count cannot equal or exceed the mass number, since the protons take up part of it, so $72$ and $104$ are impossible before any arithmetic is attempted.

The key is $40$.

Why the Other Options Are Wrong (❌):

• A. 32 · Reads Z as the neutron count
  Quotes the atomic number instead of subtracting it. $Z = 32$ is the proton count, and the neutrons are what is left of the mass number once those protons are removed, $72 - 32$, so $32$ answers a different question.
• B. 72 · Reads A as the neutron count
  Reads the mass number as a neutron count. $A = 72$ is protons and neutrons together, so it already contains the $32$ protons and overstates the neutrons by exactly that many.
• C. 104 · Addition for subtraction
  Adds the two numbers, $72 + 32 = 104$, instead of subtracting them. That would make the nucleus heavier than the mass number printed on its own label.
• E. 8 · Subtracts Z twice
  Takes the protons off and then the electrons as well, $72 - 32 - 32 = 8$. The neutral atom does have $32$ electrons, but they sit outside the nucleus and were never counted in the mass number, so $Z$ comes off once only.

Common Mistake (⚠️):
Quoting the upper number as the neutron count. The mass number is protons and neutrons added together, not neutrons alone, so $72$ silently includes the $32$ protons and overstates the neutrons by exactly that many.

Takeaway (📌):
The bottom number identifies, the top number weighs. Protons come straight from the bottom number, neutrons only from the difference, and nothing on a nuclide label ever counts neutrons for you.