Question

4 g of NaOH is dissolved in 1.0 L solution. The pH of solution is

• A. 13
• B. 1
• C. 12
• D. 7.4

Hint:

For strong bases like NaOH, the concentration of OH\(^-\) is equal to the molarity of the solution.
A quick way to calculate pH for simple concentrations like 0.1 M, 0.01 M, etc., is to first find the pOH, which will be an integer, and then subtract from 14.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We are given the mass of sodium hydroxide (NaOH), a strong base, dissolved in a specific volume of solution.
We need to calculate the pH of this solution.

Step 2: Key Formula or Approach:
1. Calculate the molar mass of NaOH.
2. Calculate the number of moles of NaOH from the given mass.
3. Calculate the molarity of the NaOH solution. Since NaOH is a strong base, this concentration is equal to the hydroxide ion concentration, \([OH^-]\).
4. Calculate the pOH using the formula: \( \text{pOH} = -\log_{10}[OH^-] \).
5. Calculate the pH using the relationship: \( \text{pH} + \text{pOH} = 14 \).

Step 3: Detailed Explanation:

1. Molar Mass of NaOH:
The atomic masses are Na = 23, O = 16, H = 1.
Molar Mass of NaOH = \(23 + 16 + 1 = 40\) g/mol.

2. Moles of NaOH:
\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{4 \text{ g}}{40 \text{ g/mol}} = 0.1 \text{ mol} \]

3. Molarity of NaOH solution:
The volume of the solution is 1.0 L.
\[ \text{Molarity [NaOH]} = \frac{\text{moles}}{\text{Volume (L)}} = \frac{0.1 \text{ mol}}{1.0 \text{ L}} = 0.1 \text{ M} \]
Since NaOH is a strong base, it dissociates completely: NaOH \(\rightarrow\) Na\(^+\) + OH\(^-\).
Therefore, the concentration of hydroxide ions is \([OH^-] = 0.1\) M or \(10^{-1}\) M.

4. Calculate pOH:
\[ \text{pOH} = -\log_{10}[OH^-] = -\log_{10}(10^{-1}) = -(-1) = 1 \]

5. Calculate pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 1 = 13 \]

Step 4: Final Answer:
The pH of the solution is 13.