What mass of sodium benzoate should be added to 140.0 mL of a 0.15 M benzoic acid solution to obtain a buffer with a pH of 4.25?

Question

Mateo Aguilar · Accepted Answer

#3.3 \ g # of sodium benzoate must be dissolved in the benzoic acid solution to obtain the solution with the desired pH (4.25).

The buffer solution is made by combining sodium benzoate and benzoic acid. To get the buffer solution with the required pH, use the Handerson-Hasselbalch equation to calculate how many moles of salt are required. The #pK_a# values for the common weak acids is provided in tables at the end of most chemistry text books. The #pK_a# value for benzoic acid is 4.20. #n_"Salt" = ??# #n_"Acid"= C_M xx V# #n_"Acid"= 0.15 \ (mol.)/Lxx 0.1400 L# #n_"Acid"= 0.0210 \ mol.# #----------------# Solve for the unknown (#n_"Salt"#) # pH = pK_a + log ((n_"Salt")/(n_"Acid"))# #4.25 = 4.20 + log ((n_"Salt")/(n_"Acid"))# #log ((n_"Salt")/(n_"Acid")) = 4.25 -4.20# #log ((n_"Salt")/(n_"Acid")) = 0.05# #(n_"Salt")/(n_"Acid") = 10^0.05# #(n_"Salt")/(n_"Acid") = 1.1# #n_"Salt" = 0.0210 xx 1.1# #n_"Salt" = 0.0231 \ mol.# #m_"Salt" = 0.0231 \ mol. xx 144.11 g/(mol.)# #m_"Salt" ~= 3.3 \ g# #3.3 \ g # of sodium benzoate must be dissolved in the benzoic acid solution to obtain the solution with the desired pH (4.25).

Axel Alvarado · Answer

undefined To calculate the mass of sodium benzoate, you can use the Henderson-Hasselbalch equation:

$$ \text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) $$

Rearrange the equation to solve for $[\text{A}^-]/[\text{HA}]$, then use the concentrations and volume to find moles, and finally, convert moles to grams using the molar mass of sodium benzoate.