Final answer:
To prepare a pH 9.90 buffer, a ratio of 1:1 NaCN to HCN is needed.
Step-by-step explanation:
To prepare a buffer solution at pH 9.90, we need to use the weak acid HCN and its conjugate base CN-. The buffer pH is determined by the pKa of the acid, which is the negative logarithm of its dissociation constant (Ka). In this case, the pKa of HCN is 9.9.
To calculate the ratio of NaCN to HCN in the buffer, we can use the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]) where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. In this equation, the ratio [A-]/[HA] is equal to the ratio of NaCN to HCN. So, to prepare the buffer, we would need a ratio of NaCN to HCN equal to the antilog of the difference between the pH and pKa. In this case, the ratio would be 10^(9.9-9.9) = 1.