What is the percent ionization in a 0.01 M HCN solution? (HCN: Ka = 4 x 10-10) (a) 0.002% (b) 0.02% (c) 0.2% (d) 2% (e) 20%

In order to determine the percent ionization in an 0.01 M HCN solution, we need to use the acid dissociation constant (Ka) value for HCN, which is 4 x 10^-10.

To calculate the percent ionization, we need to find the ratio between the concentration of the ionized form of the acid (H+) and the initial concentration of the acid (HCN) in the solution.

Since HCN dissociates into H+ and CN-, and the concentration of CN- is equal to the concentration of H+, the ratio would be the concentration of H+ divided by the initial concentration of HCN.

Now, let's calculate it step by step:

Step 1: Calculate the concentration of H+ ions produced by dissociation. Since HCN is a monoprotic weak acid, it will partially ionize in solution. So, we can assume that the concentration of H+ ions produced and the concentration of CN- ions formed are equal.

To calculate the concentration of H+ ions, we multiply the initial concentration of HCN by the percent ionization (in decimal form).

Let's denote the percent ionization as x. Therefore, the concentration of H+ ions would be 0.01 M multiplied by x.

Step 2: Set up an equation using the Ka value. The acid dissociation constant (Ka) relates the concentrations of the products (H+ and CN-) to the concentration of the reactant (HCN).

The equation for Ka is as follows: Ka = [H+][CN-] / [HCN]

Since the concentration of CN- is equal to [H+], we can write the equation as: Ka = [H+]^2 / [HCN]

Now, substitute the concentration values: 4 x 10^-10 = (x * 0.01)^2 / 0.01

Simplify the equation by multiplying both sides by 0.01: 4 x 10^-12 = x^2

Step 3: Solve for x. Taking the square root of both sides gives us: x = √(4 x 10^-12)

Calculating this value gives us: x ≈ 2 x 10^-6

Step 4: Convert x to percent. To convert x to percent, multiply it by 100. x ≈ 2 x 10^-6 * 100

x ≈ 0.0002%

Therefore, the percent ionization in an 0.01 M HCN solution is approximately 0.0002%.

HCN is a weak acid, which means it only partially dissociates into ions in water. The concentration of H+ ions is low, and the concentration of HCN is high compared to the concentration of the ions produced. The Ka value represents the extent of ionization or the tendency of the acid to dissociate. In this case, a smaller Ka value indicates a weaker acid. The percent ionization gives us the fraction of the acid that dissociates into ions. In this example, only a very small percentage of HCN molecules ionize, resulting in a low percent ionization value of around 0.0002%.