How much solid NaCN must be added to 1.0 L of a 0.5 M HCN solution to produce a solution with pH 7.0? K_a = 6.2 *10^-¹⁰ for HCN.

Question

Quizplus · Accepted Answer

Step 1: Write the balanced chemical equation for the reaction between NaCN and HCN:
NaCN + HCN ⇌ NaOH + HCN

Step 2: Write the expression for the ionization constant of HCN:
Ka = [H+][CN-]/[HCN]

Step 3: Write the expression for the pH of the solution:
pH = -log[H+]

Step 4: Use the given information to solve for the concentration of H+:
pH = 7.0
[H+] = 10^-pH = 1.0 x 10^-7 M

Step 5: Use the expression for the ionization constant to solve for the concentration of CN-:
Ka = [H+][CN-]/[HCN]
1.0 x 10^-6 = (1.0 x 10^-7) [CN-]/(0.5 - [CN-])
Simplifying the equation, we get:
[CN-] = 2.5 x 10^-6 M

Step 6: Use the concentration of CN- to calculate the amount of NaCN needed to produce this concentration:
Molarity = moles/volume (in L)
moles of NaCN = [CN-] x volume (in L)
moles of NaCN = (2.5 x 10^-6) x 1.0 = 2.5 x 10^-6 moles

Step 7: Convert moles of NaCN to grams:
mass = moles x molar mass
mass = 2.5 x 10^-6 x 49 = 1.225 x 10^-4 g

However, this is the mass of NaCN required to produce a CN- concentration of 2.5 x 10^-6 M. We need to add enough NaCN to completely react with all the HCN to produce this CN- concentration.

Step 8: Calculate the moles of HCN in 1 L of the 0.5 M solution:
moles of HCN = Molarity x volume (in L)
moles of HCN = 0.5 x 1.0 = 0.5 moles

Step 9: Calculate the moles of NaCN needed to react with all the HCN:
NaCN + HCN → NaOH + HCN
1 mole of NaCN reacts with 1 mole of HCN
moles of NaCN required = 0.5 moles

Step 10: Calculate the mass of NaCN needed to react with all the HCN:
mass of NaCN = moles x molar mass
mass of NaCN = 0.5 x 49 = 24.5 g

Therefore, the correct answer is B) 0.15 g.

How Much Solid NaCN Must Be Added to 1