**Degree of Hydrolysis of Sodium Cyanoacetate Solution**

The degree of hydrolysis of a compound measures the extent to which it undergoes hydrolysis, which is the reaction with water to produce ions. In this case, we are considering the hydrolysis of sodium cyanoacetate (NaC(O)CH2CN) in water.

**Step 1: Write the hydrolysis equation**

The hydrolysis equation for sodium cyanoacetate can be written as follows:
NaC(O)CH2CN + H2O ⇌ Na+ + C(O)CH2COO- + HCN

**Step 2: Calculate the initial concentration of sodium cyanoacetate**

The initial concentration of sodium cyanoacetate is given as 0.05 M.

**Step 3: Calculate the equilibrium concentration of sodium cyanoacetate**

The degree of hydrolysis (α) is defined as the ratio of the concentration of the hydrolyzed product to the initial concentration of the compound. In this case, the hydrolyzed product is C(O)CH2COO-.

Given that the Ka value for cyanoacetic acid (C(O)CH2CN) is 3.5 × 10^-3, we can use the Ka expression to determine the equilibrium concentration of C(O)CH2COO-.

Ka = [C(O)CH2COO-][H+]/[C(O)CH2CN]

Since the initial concentration of H+ is negligible compared to the initial concentration of C(O)CH2CN, we can assume that the concentration of H+ is approximately zero.

Therefore, the expression becomes:
Ka = [C(O)CH2COO-]/[C(O)CH2CN]

Using the Ka value, we can rearrange the equation to solve for [C(O)CH2COO-]:
[C(O)CH2COO-] = Ka × [C(O)CH2CN]

[C(O)CH2COO-] = (3.5 × 10^-3) × (0.05)

[C(O)CH2COO-] = 1.75 × 10^-4 M

**Step 4: Calculate the degree of hydrolysis**

The degree of hydrolysis (α) is the ratio of the concentration of the hydrolyzed product ([C(O)CH2COO-]) to the initial concentration of the compound ([NaC(O)CH2CN]).

α = [C(O)CH2COO-]/[NaC(O)CH2CN]

α = (1.75 × 10^-4) / (0.05)

α = 3.5 × 10^-3

Therefore, the degree of hydrolysis of a 0.05 M sodium cyanoacetate solution is 3.5 × 10^-3, which means that approximately 0.35% of the sodium cyanoacetate has undergone hydrolysis.