Question

The \(\mathrm{pK}_{\mathrm{a}}\) of \(\mathrm{NH}_{4}^{+}\) is \(9.24\), that of \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\) is \(10.64\). Is methylamine a stronger or a weaker base than ammonia? How many times stronger or weaker? What do you think this difference is due to?

Short answer

Methylamine (CH3NH2) is a stronger base than ammonia (NH3), as it has a lower pKb value (3.36) compared to ammonia (4.76). It is approximately 25 times stronger as a base. The difference in basicity can be attributed to the electron-donating inductive effect of the methyl group (-CH3), which stabilizes the positively charged conjugate acid (CH3NH3+) and increases methylamine's propensity to accept a proton.

Step-by-step solution

Calculate the pKb values for NH4+ and CH3NH3+

Using the relationship between pKa and pKb, we can calculate their pKb values: pKb(NH4+) = 14 - pKa(NH4+) = 14 - 9.24 = 4.76 pKb(CH3NH3+) = 14 - pKa(CH3NH3+) = 14 - 10.64 = 3.36

Compare the pKb values to determine the stronger base

To determine the stronger base, we need to compare the calculated pKb values: pKb(NH4+) = 4.76 pKb(CH3NH3+) = 3.36 The lower the pKb value, the stronger the base. Therefore, methylamine (CH3NH2) is a stronger base than ammonia (NH3).

Calculate the strength ratio

To find the strength ratio, calculate the difference in pKb values and use the formula: Difference in pKb values = pKb(NH4+) - pKb(CH3NH3+) = 4.76 - 3.36 = 1.40 Ratio = 10^(Difference in pKb values) = 10^1.40 ≈ 25 Methylamine (CH3NH2) is approximately 25 times stronger as a base compared to ammonia (NH3).

Discuss the possible cause of the difference

The difference in basicity between ammonia (NH3) and methylamine (CH3NH2) can be attributed to the inductive effect of the methyl group (-CH3). The methyl group's electron-donating nature stabilizes the positively charged conjugate acid (CH3NH3+) by dispersing the positive charge. This stabilization effect results in a higher propensity for methylamine to accept a proton, making it a stronger base than ammonia.

Key concepts

pKa and pKb

Understanding the concepts of pKa and pKb is crucial in acid-base chemistry. Both terms relate to the acidic or basic strength of compounds. The pKa value measures the strength of an acid, with a lower pKa indicative of a stronger acid. Conversely, pKb indicates the basicity of a substance, where a lower pKb signifies a stronger base. These two concepts are connected by the relation:\[ pK_a + pK_b = 14 \]This formula allows one to deduce the basic strength from the acidic strength or vice-versa. For instance, when given the pKa of \(\text{NH}_4^+\) and \(\text{CH}_3\text{NH}_3^+\), we can find their pKb values by subtraction from 14. This relationship highlights how pKa and pKb are linked, providing insight into the acidity and basicity of corresponding chemical species.

Inductive Effect

The inductive effect is a vital concept in understanding the differences in basicity between similar molecules. It involves the transmission of charge through a chain of atoms in a molecule, impacting electron density distribution. The presence of an electron-donating group, such as a methyl group (-CH3), can enhance the basicity of a molecule.

• This donation of electron density strengthens a base by stabilizing its conjugate acid form.
• The positive inductive effect (+I effect) from such groups increases electron availability at the nitrogen atom in methylamine, resulting in enhanced basicity.

Thus, in the case of methylamine vs. ammonia, the methyl group helps distribute the positive charge over a larger area, making methylamine a stronger base than ammonia. The inductive effect explains how substituents can influence the reactivity and properties of a compound by altering its electron cloud.

Methylamine vs. Ammonia

Comparing methylamine and ammonia helps illustrate the effect substituents have on basicity. Methylamine (CH3NH2) is a primary amine with a methyl group attached to the nitrogen, whereas ammonia (NH3) is simply the baseline compound with no such group.

• Methylamine, with its attached methyl group, exhibits a stronger basicity.
• The methyl group provides an electron-donating effect, aiding in the stabilization of the conjugate acid form, CH3NH3+.
• Ammonia, lacking this additional stabilization, is therefore a weaker base compared to methylamine.

This comparison highlights the significant impact that even a small change in structure can have on the chemical properties of a molecule. Understanding these differences is crucial for predicting reactions in organic chemistry.

Basicity Comparison

In the context of basicity, comparing two compounds helps elucidate the factors that influence chemical behaviors. Basicity relates to a compound's ability to accept protons, and comparing methylamine to ammonia, we see a clear difference.

• Calculating pKb values shows that methylamine has a pKb of 3.36, while ammonia's is 4.76.
• The lower pKb for methylamine indicates it is a stronger base.
• Quantitatively, methylamine is about 25 times more basic than ammonia, based on the pKb difference of 1.40, utilizing the formula \(10^{\text{Difference}}\ = 10^{1.40}\).

This difference underscores the impact of molecular structure on basicity. The strength ratio obtained provides insight into the reactivity and suitability of these compounds in different chemical contexts.