50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is _________.

Explanation

To solve the problem, we need to determine the amount of NaOH in 50 mL of the given sodium hydroxide solution, based on the neutralization reaction with oxalic acid. Here’s a step-by-step breakdown of the solution:

### Step 1: Write the balanced chemical equation
The reaction between oxalic acid (H₂C₂O₄) and sodium hydroxide (NaOH) can be represented as follows:
\[ \text{H}_2\text{C}_2\text{O}_4 + 2 \text{NaOH} \rightarrow \text{Na}_2\text{C}_2\text{O}_4 + 2 \text{H}_2\text{O} \]

This shows that 1 mole of oxalic acid reacts with 2 moles of sodium hydroxide.

### Step 2: Calculate the moles of oxalic acid
Given:
- Volume of oxalic acid solution = 50 mL = 0.050 L
- Molarity of oxalic acid = 0.5 M

Using the formula for moles:
\[ \text{Moles of oxalic acid} = \text{Molarity} \times \text{Volume (L)} \]
\[ \text{Moles of oxalic acid} = 0.5 \, \text{mol/L} \times 0.050 \, \text{L} = 0.025 \, \text{mol} \]

### Step 3: Determine the moles of NaOH required
From the balanced equation, we know that 1 mole of oxalic acid requires 2 moles of NaOH. Therefore:
\[ \text{Moles of NaOH} = 2 \times \text{Moles of oxalic acid} \]
\[ \text{Moles of NaOH} = 2 \times 0.025 \, \text{mol} = 0.050 \, \text{mol} \]

### Step 4: Calculate the molarity of the NaOH solution
We are given that the volume of the NaOH solution used is 25 mL = 0.025 L. Now, we can calculate the molarity of the NaOH solution:
\[ \text{Molarity of NaOH} = \frac{\text{Moles of NaOH}}{\text{Volume (L)}} \]
\[ \text{Molarity of NaOH} = \frac{0.050 \, \text{mol}}{0.025 \, \text{L}} = 2.0 \, \text{M} \]

### Step 5: Calculate the amount of NaOH in 50 mL of the solution
Now we need to find the amount of NaOH in 50 mL of this NaOH solution. First, we convert 50 mL to liters:
\[ 50 \, \text{mL} = 0.050 \, \text{L} \]

Using the molarity to find the moles in 50 mL:
\[ \text{Moles of NaOH in 50 mL} = \text{Molarity} \times \text{Volume (L)} \]
\[ \text{Moles of NaOH in 50 mL} = 2.0 \, \text{mol/L} \times 0.050 \, \text{L} = 0.1 \, \text{mol} \]

### Step 6: Calculate the mass of NaOH
The molar mass of NaOH is approximately 40 g/mol. To find the mass:
\[ \text{Mass of NaOH} = \text{Moles} \times \text{Molar Mass} \]
\[ \text{Mass of NaOH} = 0.1 \, \text{mol} \times 40 \, \text{g/mol} = 4 \, \text{g} \]

### Final Answer
The amount of NaOH in 50 mL of the given sodium hydroxide solution is **4 grams**.

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