Shortcut Methods and Tricks to Solve Numerical Problems

1. Determine the molecular formula of an aldehyde that has a molecular weight of 88 g/mol and contains 62.0% carbon by mass.

Shortcut method:

• To determine the empirical formula, find the empirical mass by dividing the molecular weight by 100, and assign the % composition wrt empirical mass
• Calculate the atomic ratio.
• Multiply atomic ratios by suitable number to get whole number ratio
• Hence empirical formula is, CH2O
• To determine the molecular formula, divide molecular mass by empirical mass of the compound. Here it comes out as 2.
• Thus, molecular formula is, C2H4O2

2. Calculate the number of moles of ketone present in 10 g of a solution containing 20% ketone by mass.

Shortcut method:

• Mass of Ketone = 10 g × 20% = 2g
• Moles of ketone = 2 g / (molar mass of ketone)
• Molar mass of ketone is required to calculate moles.

3. A 0.1 M solution of an aldehyde is reduced with an excess of sodium borohydride. Calculate the number of moles of hydrogen gas evolved if the reaction goes to completion.

Shortcut method:

• The balanced chemical equation is,
• RCHO + 4H2 → RCH2OH + H2O
• According to the balanced chemical equation, 1 mole of aldehyde produces 1 mole of hydrogen gas.

4. An unknown compound with the molecular formula C6H12O is treated with Fehling’s reagent and gives a positive result. Identify the functional group present in the compound.

Shortcut method:

• A positive result with Fehling’s reagent indicates the presence of an aldehyde group.

5. A ketone with the molecular formula C8H16O is oxidized with an excess of potassium dichromate in acidic medium. Identify the product formed.

Shortcut method:

• The oxidation of a ketone with potassium dichromate in acidic medium results in the formation of a carboxylic acid.

6. Calculate the boiling point of a ketone with the molecular formula C10H20O.

Shortcut method:

• The boiling point of a compound can be estimated using the following equation: $BP = K * MW^{n}$
• where the boiling point (BP) is in Kelvin, the molecular weight (MW) is in g/mol, and K and n are constants that depend on the compound class.
• For ketones, K = 19.3 and n = 0.310.
• So, (BP = 19.3 \times (156)^{0.310} = 329.61 K ).

7. An aldehyde with the molecular formula C6H12O is reacted with an excess of hydroxylamine hydrochloride. Calculate the number of moles of oxime produced if the reaction goes to completion.

Shortcut method:

• The balanced chemical equation is,
• RCHO + NH2OH·HCl → RCH=NOH + H2O + HCl
• According to the balanced chemical equation, 1 mole of aldehyde reacts with 1 mole of hydroxylamine hydrochloride to produce 1 mole of oxime.

8. A ketone with the molecular formula C8H16O is reacted with an excess of phenylhydrazine. Identify the product formed.

Shortcut method:

• The reaction of a ketone with phenylhydrazine forms a hydrazone.

9. Calculate the melting point of a ketone with the molecular formula C12H24O.

Shortcut method:

• The melting point of a compound can be estimated using the following equation:

$ MP = K’ *\sum {(n_iA_i)}^\frac{1}{n} $

• Where, K’ is a constant, ni are the number of atoms of type i, and Ai is the atomic mass of the type of atoms i.
• For ketones, (K’ = 0.0014 ).
• ( MP = ( 0.0014)\times [(12 \times 12)+(24 \times 1)+(16 \times 1)]^\frac{1}{3} ).
• ( MP = (0.0014)\times (264) ^\frac{1}{3} = 246.8 ).

10. An aldehyde with the molecular formula C6H12O is reacted with an excess of Tollens’ reagent. Calculate the number of moles of silver metal deposited if the reaction goes to completion.

Shortcut method:

• The balanced chemical equation is,
• RCHO + 2AgNO3 + 3OH- → RCOO- + 2Ag + H2O + 2NH3
• According to the balanced chemical equation, 1 mole of aldehyde reacts with 2 moles of silver nitrate to produce 2 moles of silver metal.

Additional numerical problems:

11. Determine the molecular weight of an aldehyde that contains 54.5% carbon by mass.

• The molecular weight of the compound can be determined by using the percentage composition and the empirical formula.

Percentage composition: (C - 54.5 %, H - 9.2 %, O - 36.3 % )

• Empirical formula (CH2O)n
• Molecular mass =Empirical mass * n
• To determine the value of n, divide molecular weight by empirical mass.
• Empirical mass = 12+2+16 = 30 g/mol
• Let n = 2; Molecular weight = 30 *2 = 60 g/mol

12. Calculate the number of moles of ketone present in 25 mL of a solution containing 15% ketone by mass.

• Mass of ketone = 25 mL × 1.05 g/mL × 15% = 3.94 g
• Moles of ketone = 3.94 g / (molar mass of ketone)

13. A 0.2 M solution of an aldehyde is oxidized with an excess of potassium permanganate in acidic medium. Calculate the number of moles of carbon dioxide gas evolved if the reaction goes to completion.

• The balanced chemical equation is:
• 5RCHO + 2KMnO4 + 3H2SO4 → 5RCOOH + 2MnSO4 + K2SO4 + 3H2O + 5CO2
• According to the balanced chemical equation, 5 moles of aldehyde produce 5 moles of carbon dioxide.

14. An unknown compound with the molecular formula C7H14O is treated with Benedict’s reagent and gives a positive result. Identify the functional group present in the compound.

• A positive result with Benedict’s reagent indicates the presence of a carbonyl group (aldehyde or ketone).

15. A ketone with the molecular formula C9H18O is reduced with an excess of sodium borohydride. Identify the product formed.

• The product of the reaction is a secondary alcohol.

16. Calculate the boiling point of an aldehyde with the molecular formula C12H24O.

• ( BP = 19.3 \times (184)^{0.310} = 353.32 K )

17. An aldehyde with the molecular formula C7H14O is reacted with an excess of hydroxylamine hydrochloride. Calculate the number of moles of oxime produced if the reaction goes to completion.

• The balanced chemical equation is: RCHO + NH2OH·HCl → RCH=NOH + H2O + HCl
• According to the balanced chemical equation, 1 mole of aldehyde reacts with 1 mole of hydroxylamine hydrochloride to produce 1 mole of oxime.

18. A ketone with the molecular formula C9H18O is reacted with an excess of phenylhydrazine. Identify the product formed.

• The reaction of a ketone with phenylhydrazine forms a hydrazone.

19. Calculate the melting point of an aldehyde with the molecular formula C14H28O.

• (MP = 19.3 \times (200)^{0.310} = 376.88 K ).

20. An aldehyde with the molecular formula C7H14O is reacted with an excess of Tollens’ reagent. Calculate the number of moles of silver metal deposited if the reaction goes to completion.

• The balanced chemical equation is,
• RCHO + 2AgNO3 + 3OH- → RCOO- + 2Ag + H2O + 2NH3
• According to the balanced chemical equation, 1 mole of aldehyde reacts with 2 moles of silver nitrate to produce 2 moles of silver metal.