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

Verified step by step guidance

1. Identify the components of the buffer solution: dimethylamine (a weak base) and dimethylammonium chloride (its conjugate acid).
2. Use the Henderson-Hasselbalch equation for a buffer solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \).
3. 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.
4. Rearrange the Henderson-Hasselbalch equation to solve for the ratio \( \frac{[\text{Base}]}{[\text{Acid}]} \): \( \frac{[\text{Base}]}{[\text{Acid}]} = 10^{(\text{pH} - \text{pK}_a)} \).
5. Calculate the relative masses of dimethylamine and dimethylammonium chloride needed using the molar masses and the ratio obtained from the Henderson-Hasselbalch equation.