Question

You are asked to prepare 3.4 L of a HCN/NaCNbuffer that has a pH of 9.69 and an osmotic pressure of 1.59 atm at 298 K. What masses of HCN and NaCN should you use to prepare the buffer? (Assume complete dissociation of NaCN.)

Answer 1

First, apply buffer equation, since this contains weak acid HCN + conjugate base NaCN

pH = pKa + log(NaCN/HCN)

pKa for HCN = 9.21

9.69 = 9.21 + log(NaCN/HCN)

10^(9.69-9.21) = (NaCN/HCN)

NaCN/HCN = 3.01995

now... relate with another equation

Posmotic = i*M*RT

i = 2 ions + 1 molecule = 3 (HCN and Na+ and CN- will be found in solution)

M = total molarity

R = .082 Latm/molK

T = 298k

substitute

Posmotic = i*M*RT

M = Psom /(iRT)

M = 1.59/(3*0.082*298)

M = 0.021689

total Molarity --> 0.021689 M

total moeles M*V = 0.021689*3.4 = 0.0737426 moles of HCN and NaCN required

and we know the ratio

NaCN/HCN = 3.01995

so

HCN + NaCN = 0.0737426

NaCN = 3.01995 *HCN

HCN + 3.01995 *HCN= 0.0737426

HCN = 0.0737426 /(1+3.01995 ) = 0.018344 moles

NaCN = 3.01995 *HCN =3.01995 * 0.018344 = 0.0553 moles

masses:

mass of HCN = mol*MW = 0.018344 *27.0253 = 0.4957g

mass of NaCN = mol*MW = 0.0553 *49.01 = 2.710253 g