A solution of sodium cyanide, NaCN, has a pH of 11.20. How many grams of NaCN are in 835 mL of a solution with the same pH?

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A solution of sodium cyanide, NaCN, has a pH of 11.20. How many grams of NaCN are in 835 mL of a solution with the same pH?

**Educational Lab Exercise: Calculating the Mass of Sodium Cyanide in Solution**

---

### Problem Statement

A solution of sodium cyanide, NaCN, has a pH of 11.20. How many grams of NaCN are in 835 mL of a solution with the same pH?

Given:
- \( K_b \) (CN\(^-\)) = \( 1.7 \times 10^{-5} \)

**Mass of NaCN (g):** 
\[ \boxed{ \quad \quad } \]

---

### Steps to Solve:

1. **pH to pOH Conversion**: Given the pH, first find the pOH.
   \[
   \text{pOH} = 14 - \text{pH}
   \]
   Substitute pH = 11.20:
   \[
   \text{pOH} = 14 - 11.20 = 2.80
   \]

2. **Hydroxide Ion Concentration**: Calculate the concentration of OH\(^-\) ions:
   \[
   \left[ \text{OH}^- \right] = 10^{-\text{pOH}} = 10^{-2.80}
   \]

3. **Henderson-Hasselbalch Equation**:
   Using the equilibrium expression of the weak base:
   \[
   K_b = \frac{\left[ \text{OH}^- \right] \left[ \text{HCN} \right]}{\left[ \text{CN}^- \right]}
   \]
   Since the problem involves the complete dissociation of NaCN:
   \[
   \left[ \text{CN}^- \right] = \left[ \text{OH}^- \right]
   \]

4. **Equilibrium Concentration**:
   \(
   \left[ \text{OH}^- \right] = \sqrt{ K_b \times \text{initial concentration of NaCN} }
   \)
   Plugging in the known values will let us find the initial concentration of NaCN, and subsequently using:
   \[
   \text{initial concentration of NaCN} (\text{mol/L}) = \frac{\text{mass of NaCN}}{ \text{molar mass of NaCN} } \times \frac{1}{\text{Volume in Liter}}
Transcribed Image Text:**Educational Lab Exercise: Calculating the Mass of Sodium Cyanide in Solution** --- ### Problem Statement A solution of sodium cyanide, NaCN, has a pH of 11.20. How many grams of NaCN are in 835 mL of a solution with the same pH? Given: - \( K_b \) (CN\(^-\)) = \( 1.7 \times 10^{-5} \) **Mass of NaCN (g):** \[ \boxed{ \quad \quad } \] --- ### Steps to Solve: 1. **pH to pOH Conversion**: Given the pH, first find the pOH. \[ \text{pOH} = 14 - \text{pH} \] Substitute pH = 11.20: \[ \text{pOH} = 14 - 11.20 = 2.80 \] 2. **Hydroxide Ion Concentration**: Calculate the concentration of OH\(^-\) ions: \[ \left[ \text{OH}^- \right] = 10^{-\text{pOH}} = 10^{-2.80} \] 3. **Henderson-Hasselbalch Equation**: Using the equilibrium expression of the weak base: \[ K_b = \frac{\left[ \text{OH}^- \right] \left[ \text{HCN} \right]}{\left[ \text{CN}^- \right]} \] Since the problem involves the complete dissociation of NaCN: \[ \left[ \text{CN}^- \right] = \left[ \text{OH}^- \right] \] 4. **Equilibrium Concentration**: \( \left[ \text{OH}^- \right] = \sqrt{ K_b \times \text{initial concentration of NaCN} } \) Plugging in the known values will let us find the initial concentration of NaCN, and subsequently using: \[ \text{initial concentration of NaCN} (\text{mol/L}) = \frac{\text{mass of NaCN}}{ \text{molar mass of NaCN} } \times \frac{1}{\text{Volume in Liter}}
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