Chemistry: An Atoms-Focused Approach
Chemistry: An Atoms-Focused Approach
14th Edition
ISBN: 9780393912340
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 11, Problem 11.76QA
Interpretation Introduction

To find:

a) Molar mass of caffeine.

b) Molecular formula of caffeine.

Expert Solution & Answer
Check Mark

Answer to Problem 11.76QA

Solution:

a) The molar mass of caffeine is 193.97 g/mol.

b) The molecular formula of caffeine is C8H10N4O2.

Explanation of Solution

1) Concept:

2) Given:

i) Mass of caffeine solution = 150 mg

ii) Solvent used =10.0 g camphor = 0.01 kg  (since 1 kg = 1000 g)

iii) Tf=3.07 

iv) Kf of  camphor=39.7 mol

v) Caffeine is a non-electrolyte. This suggests that, the van’t Hoff factor (i) for caffeine acid is 1.

vi) % Mass of C = 49.49

vii) % Mass of H = 5.15

viii) % Mass of N = 28.87

3) Formula:

Formula for depression in freezing point is:

Tf=Kf x i  x m

Where, Tf represents depression in freezing point, Kf represents freezing point depression constant, i = van’t Hoff factor, m = molality of solution

Formula for molality is:

Molality m= moles of solute (mol)mass of solvent (kg)

4) Calculations:

a)

Calculate Molar mass of Caffeine:

Solving above equation for molality, we get,

3.07 =39.7  m x 1 x m

m= 3.07 39.7  / m 

m=0.0773 m

We find moles of solute caffeine using calculated molality and mass of solvent as:

0.0773 m= moles of solute0.01 kg camphor

moles of solute=0.000773 mol of Caffeine

Molar mass is the mass in grams per mole of that substance, so it will be:

0.150 g0.000773 moles  =193.97g/mol

The molar mass of Caffeine is 193.97 g/mol.

b)

Molecular formula of caffeine:

Given:

% Mass of C = 49.49

% Mass of H = 5.15

% Mass of N = 28.87

Consider the mass of caffeine  = 100 g

Therefore,

Mass of C = 100 g ×49.49100=49.49 g

Mass of H = 100 g × 5.15100=5.15 g

Mass of N =100 g × 28.87100= 28.87 g

And remaining is Oxygen

i. Calculate mass of oxygen:

From these given masses we would find out mass of oxygen as,

Mass of caffeine = Mass of C + Mass of H + Mass of N + Mass of O

100 g = 49.49 g + 5.15 g + 28.87 g + Mass of O

Mass of O = 100 g  83.51 g

Mass of O= 16.49 g

ii. Calculate moles of each atom:

We can calculate the moles of each using the mass in g.

49.49 g C x 1 mol of C12.01 g C  =4.1205 mol C

5.15 g H x 1 mol of H1.008 g H  =5.1091 mol H

28.87 g N x 1 mol of N14.01 g N  =2.0612 mol N

16.49 g O x 1 mol of O16.00 g O  =1.0307 mol O

iii. Find out empirical formula:

Comparing moles of C, H and O, we observe that moles of O are the least. So, atoms of C, H and O are calculated by dividing each of the moles by least amount of moles.

Carbon atoms= 4.1205 mol C1.0307 mol O=3.9984

Hydrogen atoms= 5.1091 mol H1.0307 mol O=4.965

Nitrogen atoms= 2.0612 mol N1.0307 mol O=1.99982

Oxygen atoms= 1.0307 mol O1.0307 mol O=1

Thus empirical formula for caffeine is C4H5N2O.

iv. Find out molecular formula:

We have calculated the molar mass of caffeine in part a) = 193.97 g/mol

Empirical formula mass = 412.01+ 51.008+ 214.01+ 116.00

Empirical formula mass= 97.1 g/mol

Empirical formula unit n= Molar mass Empirical formula mass

Empirical formula unit n= 193.91 g/mol97.1 g/mol=1.997=2

Molecular formula = Empirical formula unit (n) × Empirical formula

Molecular formula=2 × C4H5N2O

Molecular formula=C8H10N4O2

The molar mass of caffeine is 193.97 g/mol.

The molecular formula of caffeine is C8H10N4O2.

Conclusion:

Freezing point depression is a colligative property which is useful in determining the molar mass of the solute in a solution. Using stoichiometry between a compound and its constituent elements, one can determine the empirical formula and molecular formula of the unknown substance.

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Chapter 11 Solutions

Chemistry: An Atoms-Focused Approach

Ch. 11 - Prob. 11.12QACh. 11 - Prob. 11.13QACh. 11 - Prob. 11.14QACh. 11 - Prob. 11.15QACh. 11 - Prob. 11.16QACh. 11 - Prob. 11.17QACh. 11 - Prob. 11.18QACh. 11 - Prob. 11.19QACh. 11 - Prob. 11.20QACh. 11 - Prob. 11.21QACh. 11 - Prob. 11.22QACh. 11 - Prob. 11.23QACh. 11 - Prob. 11.24QACh. 11 - Prob. 11.25QACh. 11 - Prob. 11.26QACh. 11 - Prob. 11.27QACh. 11 - Prob. 11.28QACh. 11 - Prob. 11.29QACh. 11 - Prob. 11.30QACh. 11 - Prob. 11.31QACh. 11 - Prob. 11.32QACh. 11 - Prob. 11.33QACh. 11 - Prob. 11.34QACh. 11 - Prob. 11.35QACh. 11 - Prob. 11.36QACh. 11 - Prob. 11.37QACh. 11 - Prob. 11.38QACh. 11 - Prob. 11.39QACh. 11 - Prob. 11.40QACh. 11 - Prob. 11.41QACh. 11 - Prob. 11.42QACh. 11 - Prob. 11.43QACh. 11 - Prob. 11.44QACh. 11 - Prob. 11.45QACh. 11 - Prob. 11.46QACh. 11 - Prob. 11.47QACh. 11 - Prob. 11.48QACh. 11 - Prob. 11.49QACh. 11 - Prob. 11.50QACh. 11 - Prob. 11.51QACh. 11 - Prob. 11.52QACh. 11 - Prob. 11.53QACh. 11 - Prob. 11.54QACh. 11 - Prob. 11.55QACh. 11 - Prob. 11.56QACh. 11 - Prob. 11.57QACh. 11 - Prob. 11.58QACh. 11 - Prob. 11.59QACh. 11 - Prob. 11.60QACh. 11 - Prob. 11.61QACh. 11 - Prob. 11.62QACh. 11 - Prob. 11.63QACh. 11 - Prob. 11.64QACh. 11 - Prob. 11.65QACh. 11 - Prob. 11.66QACh. 11 - Prob. 11.67QACh. 11 - Prob. 11.68QACh. 11 - Prob. 11.69QACh. 11 - Prob. 11.70QACh. 11 - Prob. 11.71QACh. 11 - Prob. 11.72QACh. 11 - Prob. 11.73QACh. 11 - Prob. 11.74QACh. 11 - Prob. 11.75QACh. 11 - Prob. 11.76QACh. 11 - Prob. 11.77QACh. 11 - Prob. 11.78QACh. 11 - Prob. 11.79QACh. 11 - Prob. 11.80QACh. 11 - Prob. 11.81QACh. 11 - Prob. 11.82QACh. 11 - Prob. 11.83QACh. 11 - Prob. 11.84QA
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