An organic compound containing carbon, hydrogen, and nitrogen was analyzed and found to co… — JAMB UTME

An organic compound containing carbon, hydrogen, and nitrogen was analyzed and found to contain $61.02\%$ carbon and $15.25\%$ hydrogen by mass, with the remainder being nitrogen. Given that the relative molecular mass of the compound is $118\text{ g/mol}$ , what is the value of the integer multiplier $n$ that relates its empirical formula to its molecular formula? $[C = 12, H = 1, N = 14]$

Answer: 2

Answer

The value of the integer multiplier n is 2.

Subtracting the carbon (

61.02\%

) and hydrogen (

15.25\%

) percentages from

100\%

gives a nitrogen content of

23.73\%

. Converting these mass percentages to mole ratios by dividing by relative atomic masses (

C=12, H=1, N=14

) gives

5.085\text{ mol}

of C,

15.25\text{ mol}

of H, and

1.695\text{ mol}

of N. Dividing by the smallest value (

1.695

) produces the mole ratio

3:9:1

, establishing the empirical formula as

C_3H_9N

. The empirical mass is

(3 \times 12) + (9 \times 1) + 14 = 59\text{ g/mol}

. Dividing the relative molecular mass (

118\text{ g/mol}

) by the empirical mass (

59\text{ g/mol}

) yields

n = 2

Step-by-Step Solution

Calculate percentage composition of nitrogen

23.73%

The sum of percentages of all constituent elements in a compound must equal 100%.

Calculate relative number of moles for each element

C = 5.085 mol, H = 15.25 mol, N = 1.695 mol

Dividing the mass percentage of each element by its relative atomic mass gives its relative mole quantity.

Determine simplest whole number atomic ratio

C : H : N = 3 : 9 : 1

Dividing all mole amounts by the smallest value (1.695) gives the empirical mole ratio.

Determine the empirical formula mass

59 g/mol

Summing the atomic masses of elements in C3H9N yields (3 x 12) + (9 x 1) + 14 = 59 g/mol.

Calculate the integer multiplier n

Dividing relative molecular mass (118 g/mol) by empirical formula mass (59 g/mol) gives n = 2.

Key Concept

Calculation of Empirical Formula and Molecular Formula Multiplier

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