Chapter 1

Question 1

Describe errors that may cause an observed capillary melting point of a pure sample to be LOWER than the correct melting point.

Answer 1

• Heating the sample too quickly (lag between real temperature and what thermometer reads)
• Using an uncalibrated thermometer
• Measuring a sample with an impurity
• Measuring a wet sample

Question 2

Describe errors that may cause an observed capillary melting point of a pure sample to be HIGHER than the correct melting point.

Answer 2

• Using too large a sample size
• Packing a sample too loosely in the capillary tube
• Using an uncalibrated thermometer
• Measuring a sample with significant quantities of an impurity with much higher melting point than sample itself

Question 3

Describe errors that may cause an observed capillary melting point of a pure sample to be BROAD in range (over several degrees).

Answer 3

• Measuring an impure sample
• Measuring a wet sample
• Heating the sample too quickly
• Using too large a sample size
• Measuring a sample with large crystals

Question 4

True/False

An impurity always lower the melting point of an organic compound

Answer 4

False

Note: Usually true, except if impurity has a significantly higher m.p. and is present in large quantities

Question 5

True/False

A sharp melting point for a crystalline organic substance always indicated a pure single compound

Answer 5

False

Note: Usually true with the exception of eutectic mixture

Question 6

True/False

If the addition of a sample of compound A to compound X does not lower the melting point of X, X must be identical to A.

Answer 6

True

Note: Rare exception. If A has a higher melting temperature than X, and the addition of A to X creates a mixture with the same melting point as pure A, then the statement could be false (unlikely)

Question 7

True/False

If the addition of a sample of compound A to compound X does lowers the melting point of X, X and A cannot be identical.

Answer 7

True

Question 8

The melting points of pure benzoic acid and pure 2-naphtol are 122.5°C and 123°C, respectively. Given a pure sample that is known to be either pure benzoic acid or pure 2-naphtol, describe a procedure you might use to determine the identity of the sample.

Answer 8

Prepare 2 new samples (A and B), A with a mix of your pure sample and sample of benzoic acid, and B with a mix of your pure sample and a sample of 2-naphtol. Measure both melting points. If the melting point of the sample is broad and depressed, then that sample (A or B) is likely a mixture. If the melting point of the sample is sharp and the same temperature, then the sameple (A or B) is likely a pure sample (i.e. the 2 compounds in the mixture are identical).

Question 9

Derive the mathematical relationship between frequency and wavenumber by using Equations 8.1 (E=Nhv=Nh(c/λ)) & 8.3 (ṽ(cm^-1) = 10000/λ(µm)) and point out why it is imprecise to use the terms “frequency” and “wavenumber” interchangeably.

Answer 9

Equation 8.1

E=Nhv = Nh(c/λ)

Divide both sides by Nh, then get: v(s^-1) = c(cm/s) / λ(cm)

Equation 8.3

ṽ(cm^-1) = 10000/λ(µm)

Convert µm to cm (factor of 10000), then get: ṽ (cm^-1) = 1 / λ(cm)

Rearrange to get: λ(cm) = 1 / ṽ (cm^-1)

Combined Equation of 8.1 & 8.3

v = c / (1 /ṽ (cm^-1)) = cṽ

Final Equation

v (s^-1) = c(cm/s) x ṽ (cm^-1)

It is incorrect to use the two interchangeably b/c they are in different units (frequency = s^-1; wavenumber = cm^-1)

Question 10

Compute the reduced mass, m*, of a C-D bond and then use Equation 8.4 to determine the wavenumber at which the C-D stretching vibration occurs, assuming the corresponding vibration for the C-H bond is 3000cm^-1.

Answer 10

Reduced mass Equation

Reduced mass m* = (m_Catom x m_Datom) / (m_Catom + m_Datom​)

Solve for m:

m* = (12g/mol / 6.022 x 10²³atom/mol) x (2g/mol / 6.022 x 10²³atom/mol)

(12g/mol / 6.022 x 10²³atom/mol) + (2g/mol / 6.022 x 10²³atom/mol)

m* = 2.85 x 10^-24g/atom

Equation 8.4

ṽ = (1 / 2πc) x sqrt k / m*

ṽ = (1 / (2π)(3 x 10¹⁰cm/s)) x sqrt (5 x 10⁵dyne/cm / 2.85 x 10^-24g/atom)

ṽ = 2225cm^-1