Determination of pH for a 0.295 M Solution of Methylamine (CH3NH2) with a Base Dissociation Constant (Kb) of 4.38 x 10^-4

Introduction

Methylamine (CH3NH2) is a weak base and its behavior in an aqueous solution can be quantitatively described by the base dissociation constant (Kb). This article will determine the pH of a 0.295 M solution of methylamine, given its Kb value of 4.38 x 10^-4. The calculations will involve equilibrium constants, ionization expressions, and approximations to find the correct pH.

H2O and CH3NH2 System

The chemical reaction for the ionization of methylamine in water can be represented as:

CH3NH2(aq) H2O(l) ? CH3NH3 (aq) OH-(aq)

The equilibrium expression for this reaction is:

Kb [CH3NH3 ][OH-]/[CH3NH2]

Calculating the Hydroxide Ion Concentration [OH-]

Let's assume that x mol/L is the concentration of methylamine that dissociates. At equilibrium: [CH3NH3 ] x [OH-] x [CH3NH2] 0.295 - x

Substitute these into the Kb expression:

Kb x^2 / (0.295 - x)

For simplicity, assume 0.295 - x is approximately 0.295 (since x is small compared to 0.295):

4.38 x 10^-4 x^2 / 0.295

x √(4.38 x 10^-4 * 0.295) 0.0114 mol/L

This approximation is reasonable, as the calculated x value is small. Now, find the pOH and then pH:

pOH -log([OH-]) -log(0.0114) 1.94

pH 14 - pOH 14 - 1.94 12.06

Checking for Accuracy

Using the same expression, calculate a second approximation:

Kb x^2 / (0.295 - 0.0114) 4.38 x 10^-4

x √(4.38 x 10^-4 * 0.2836) 0.0111 mol/L

This value is slightly smaller, but the difference is minimal, confirming the accuracy of the first approximation.

Interrogating the Base Association Equilibrium

For a more detailed understanding, let's write the base association equilibrium:

CH3NH2(aq) H2O(l) ? CH3NH3 (aq) OH-(aq)

The equilibrium expression:

Kb [CH3NH3 ][OH-] / [CH3NH2]

If x mol/L is the concentration of methylamine that dissociates, then:

Kb x^2 / (0.295 - x)

Assuming 0.295 - x ≈ 0.295:

4.38 x 10^-4 x^2 / 0.295

x √(4.38 x 10^-4 * 0.295) 0.0114 mol/L

pOH -log(0.0114) 1.94

pH 14 - 1.94 12.06

Discussion on pH

The pH of the 0.295 M methylamine solution is 12.06. This value is significantly basic, as expected for a strong base. This pH is higher than 7, indicating that methylamine acts as a base in water.

Additional information regarding the pKa of methyl ammonium hydrochloride (CH3NH3Cl) and the relationship between pKa and pKb is provided to offer a more comprehensive understanding. The pKa of methyl ammonium hydrochloride is given as 10.73, from which one can calculate the pKb as 3.27 using the relationship pKa pKb 14. This value is consistent with the calculated pH of the methylamine solution.

Conclusion

The pH of a 0.295 M solution of methylamine, given its base dissociation constant (Kb), is approximately 12.06. This value is influenced by the extent of ionization and can be calculated through equilibrium chemistry and approximations. Understanding these concepts can help in predicting and calculating the behavior of weak bases in aqueous solutions.