What relative masses of dimethylamine and dimethylammonium chloride are needed to prepare a buffer solution with a pH of 10.43?

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Identify the components of the buffer solution: dimethylamine (a weak base) and dimethylammonium chloride (its conjugate acid).

Use the Henderson-Hasselbalch equation for a buffer solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \).

Find the \( \text{pK}_a \) of dimethylammonium chloride. This can be done by using the relationship \( \text{pK}_a + \text{pK}_b = 14 \), where \( \text{pK}_b \) is for dimethylamine.

Rearrange the Henderson-Hasselbalch equation to solve for the ratio \( \frac{[\text{Base}]}{[\text{Acid}]} \): \( \frac{[\text{Base}]}{[\text{Acid}]} = 10^{(\text{pH} - \text{pK}_a)} \).

Calculate the relative masses of dimethylamine and dimethylammonium chloride needed using the molar masses and the ratio obtained from the Henderson-Hasselbalch equation.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, dimethylamine acts as the weak base, while dimethylammonium chloride serves as its conjugate acid, allowing the solution to maintain a stable pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base and [HA] is the concentration of the acid. This equation is essential for determining the relative amounts of dimethylamine and dimethylammonium chloride needed to achieve the desired pH of 10.43.

pKa and pH Relationship

The pKa is the negative logarithm of the acid dissociation constant (Ka) and indicates the strength of an acid in solution. The relationship between pKa and pH is crucial for buffer preparation, as it helps determine how much of the acid and base components are required to achieve a specific pH. For dimethylammonium chloride, knowing its pKa allows for the calculation of the necessary concentrations of both components to maintain the target pH.

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