What mass of ammonium chloride should be added to 2.55 L of 0.155 M NH3 to obtain a buffer with a pH of 9.55? (Assume no volume change.)

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Identify the components of the buffer system: Ammonia (NH_3) is a weak base, and ammonium chloride (NH_4Cl) will provide the conjugate acid, NH_4^+.

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 the ammonium ion (NH_4^+). The \( \text{pK}_a \) is related to the \( \text{pK}_b \) of NH_3 by the equation \( \text{pK}_a + \text{pK}_b = 14 \).

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 moles of NH_3 in the solution using its concentration and volume, then use the ratio from the Henderson-Hasselbalch equation to find the moles of NH_4^+ needed. Convert this to mass using the molar mass of NH_4Cl.

Key Concepts

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

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, the buffer is formed using ammonia (NH3) as the weak base and ammonium chloride (NH4Cl) as its conjugate acid.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acidic and basic components. 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 calculating the required concentrations of NH3 and NH4Cl to achieve the desired pH.

Molarity and Mass Calculations

Molarity (M) is a measure of concentration defined as moles of solute per liter of solution. To find the mass of ammonium chloride needed, one must first calculate the number of moles required using the desired concentration and volume, and then convert moles to mass using the molar mass of NH4Cl. This step is crucial for preparing the buffer solution accurately.

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