Physical Chemistry Numericals: 5 Formula Practice MCQs
This post gives you five physical chemistry numericals in MCQ form, each with a full solution.
You will also learn a simple routine to check every step of your own working against an answer key.
Why numericals go wrong
A numerical is a question where you must calculate a value using a formula. Physical chemistry is full of them: gases, solutions, thermodynamics and kinetics.
Students usually lose marks in four places:
- Mixing units, such as joules with kilojoules, or millilitres with litres.
- Using the wrong value of the gas constant for the unit of pressure.
- Dropping a sign, especially in free energy and enthalpy questions.
- Rounding too early, so the final answer drifts away from the options.
The formulas themselves are short. So the habit you must build is a fixed order of work. Use the same order for every problem.
A four-step routine for every numerical
- Write the formula before you write any number. If you cannot recall it, you have found a revision gap.
- List the data with units. Convert at this stage, not later.
- Substitute and simplify one line at a time. Keep units in the lines so you can see them cancel.
- Check the answer for sense. Is the sign right? Is the size reasonable? Does it match one option only?
Now apply this routine to the five problems. Attempt each one before reading the solution.
Five practice numericals with solutions
Q1. Ideal gas equation. How many moles of an ideal gas are present in 12.3 L at 2 atm and 300 K? (Take R = 0.082 L atm K-1 mol-1.)
(a) 0.5 mol (b) 1.0 mol (c) 2.0 mol (d) 4.0 mol
Solution. Formula: PV = nRT, so n = PV / RT.
n = (2 × 12.3) / (0.082 × 300) = 24.6 / 24.6 = 1.0 mol.
Answer: (b). The unit of R already fits atm and litres, so no conversion was needed.
Q2. Molarity. 4 g of NaOH (molar mass 40 g mol-1) is dissolved in water to make 500 mL of solution. What is its molarity?
(a) 0.1 M (b) 0.2 M (c) 0.4 M (d) 0.8 M
Solution. Molarity is moles of solute per litre of solution.
Moles = 4 / 40 = 0.1 mol. Volume = 500 mL = 0.5 L.
M = 0.1 / 0.5 = 0.2 mol L-1.
Answer: (b). Option (a) is the trap for students who divide by 1 L and forget to convert 500 mL to 0.5 L.
Q3. Gibbs free energy. For a reaction, ΔH = −40 kJ mol-1 and ΔS = −100 J K-1 mol-1. Find ΔG at 300 K.
(a) −70 kJ mol-1 (b) −10 kJ mol-1 (c) +10 kJ mol-1 (d) +70 kJ mol-1
Solution. Formula: ΔG = ΔH − TΔS.
Convert first: ΔS = −100 J K-1 mol-1 = −0.1 kJ K-1 mol-1.
TΔS = 300 × (−0.1) = −30 kJ mol-1.
ΔG = −40 − (−30) = −10 kJ mol-1.
Answer: (b). Option (a) comes from losing the minus sign of ΔS.
Q4. Depression of freezing point. 18 g of glucose (molar mass 180 g mol-1) is dissolved in 1 kg of water. Find the fall in freezing point. (The cryoscopic constant of water is 1.86 K kg mol-1.)
(a) 0.093 K (b) 0.186 K (c) 0.372 K (d) 1.86 K
Solution. Formula: fall in freezing point = cryoscopic constant × molality. Molality is the moles of solute per kg of solvent.
Moles of glucose = 18 / 180 = 0.1 mol. Mass of solvent = 1 kg, so molality = 0.1 mol kg-1.
Fall in freezing point = 1.86 × 0.1 = 0.186 K.
Answer: (b). Glucose does not split into ions in water, so no extra factor is needed.
Q5. First-order kinetics. A first-order reaction is 75% complete in 40 minutes. Find its rate constant. (Use ln 2 = 0.693.)
(a) 0.0173 min-1 (b) 0.0347 min-1 (c) 0.0693 min-1 (d) 0.139 min-1
Solution. If 75% has reacted, 25% is left. That is one-fourth, which is two half-lives (100% to 50% to 25%).
So 2 × t1/2 = 40 min, and t1/2 = 20 min.
For a first-order reaction, k = 0.693 / t1/2 = 0.693 / 20 = 0.03465, which is about 0.0347 min-1.
Answer: (b). Option (a) comes from using 40 min as the half-life.
Common traps at a glance
| Topic | Formula | Unit check before substituting |
|---|---|---|
| Ideal gas | PV = nRT | Match R to the units of P and V |
| Molarity | moles / volume in litres | Change mL to L |
| Free energy | ΔG = ΔH − TΔS | Put ΔH and ΔS in the same energy unit |
| Freezing point fall | constant × molality | Use kg of solvent, not litres of solution |
| First-order rate constant | k = 0.693 / t1/2 | Count half-lives correctly first |
How to verify your steps using an answer key
Getting the right option is good. Getting it for the right reason is better. A lucky guess teaches you nothing.
On the Dreamers Quiz portal you pick a class or exam, attempt the set against the clock, and then see your score and the answer key. You can attempt as many times as you like. Use this in a planned way:
- Solve on paper first. Write all four routine steps for each question, even in a timed set.
- Mark your answers, then open the key. For every wrong answer, do not just read the correct option.
- Find the exact line where you went off. Work backwards from the key's option. Ask which step would give that value, and which step gave your value instead.
- Name the error type. Was it a unit, a sign, a formula or an arithmetic slip? Keep a small tally in your notebook.
- Re-attempt the set later. Since repeat attempts are allowed, check that the same error does not return.
Also check the right answers. If you got a question correct but could not explain each line, treat it as half-correct and revise that topic.
Using the sets before school tests and entrance exams
The portal suggests three uses: chapter revision before a school test, a quick check after a class, and speed practice for the NEET and CUET MCQ sections.
My advice is to match the use to the stage. Right after a class, do a short set and focus on method. Before a test, do chapter sets and focus on accuracy. Closer to an entrance exam, focus on speed, but only after your accuracy is steady. Speed built on weak method just produces wrong answers faster.
Keep the NCERT chapter open while you practise. If a numerical uses a formula you cannot derive or recall, go back to the textbook explanation and then return to the problem.
Key takeaways
- Follow one fixed order: formula, data with units, substitution, sense check.
- Convert units at the data stage. Most wrong options are built from unit and sign errors.
- Use the answer key to trace your error to a specific line, not only to learn the correct option.
- Name each error type and keep a tally. Repeated errors show what to revise.
- Build accuracy first, then speed.
Frequently asked questions
Which value of R should I use?
It depends on the units of the problem. In Q1, pressure was in atm and volume in litres, so R = 0.082 L atm K-1 mol-1 was the right choice. Always check the unit of R before substituting.
Why did Q3 need a unit change?
ΔH was given in kJ and ΔS in J. You cannot subtract TΔS from ΔH until both are in the same unit. Here, converting ΔS to kJ was the safest step.
Can I attempt the same quiz set more than once?
Yes. The portal says you can attempt as many times as you like. Use repeat attempts to confirm that you have fixed your earlier errors.
Is this practice useful for NEET and CUET?
The portal lists speed practice for the NEET and CUET MCQ sections as one of its uses. Numericals like these also build the calculation habits those papers reward, but no practice can promise a particular result.
What should I do if my answer is not among the options?
Do not force a match. Recheck units first, then signs, then arithmetic. If it is still off, redo the problem from the formula line.
What to do next. Try it yourself on the page below.
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