What mass of KNO2 must be added to create 200.0 mL of a buffer solution with a pH of 3.00 and an HNO2 concentration of 0.150 M? The pKₐ of nitrous acid is 3.34.

• A. 0.024 g
• B. 0.012 g
• C. 0.096 g
• D. 0.048 g

Answer: (D)

Verified step by step guidance

1. First, understand that a buffer solution consists of a weak acid and its conjugate base. In this case, HNO2 is the weak acid and KNO2 provides the conjugate base NO2⁻.
2. Use the Henderson-Hasselbalch equation to relate the pH of the buffer solution to the concentrations of the acid and its conjugate base: $p_H=p_K+log\left(\frac{[A_{-}}{[{\mathrm{HA}}_{]}}\right)$, where $p_K$ is the acid dissociation constant, $[{\mathrm{HA}}_{]}$ is the concentration of the acid, and $[A_{-}$ is the concentration of the conjugate base.
3. Rearrange the Henderson-Hasselbalch equation to solve for the concentration of the conjugate base NO2⁻: $[A_{-}=[{\mathrm{HA}}_{]}$.
4. Substitute the given values into the equation: $[A_{-}=0.150\times {10}^{3.00-3.34}$. Calculate the concentration of NO2⁻.
5. Convert the concentration of NO2⁻ to mass using the molar mass of KNO2. First, calculate the moles of NO2⁻ in 200.0 mL of solution, then use the molar mass of KNO2 to find the mass: $\mathrm{mass}=\mathrm{moles}\times \mathrm{molar\; mass}$.