How many moles of `Na^(+)` ions are in `20mL "of" 0.40" "M " "Na_(3)PO_(4)` .

Options

A. `0.0080`
B. `0.024`
C. `0.050`
D. `0.20`

Explanation

To find out how many moles of \( \text{Na}^+ \) ions are in 20 mL of 0.40 M \( \text{Na}_3\text{PO}_4 \), we can follow these steps:

### Step 1: Calculate the number of moles of \( \text{Na}_3\text{PO}_4 \)

First, we need to determine the number of moles of \( \text{Na}_3\text{PO}_4 \) in the given volume.

The formula to calculate the number of moles is:

\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in liters)} \]

Given:
- Molarity (M) = 0.40 M
- Volume (V) = 20 mL = 0.020 L (since 1 L = 1000 mL)

Now, substituting the values:

\[ \text{Number of moles of } \text{Na}_3\text{PO}_4 = 0.40 \, \text{mol/L} \times 0.020 \, \text{L} = 0.008 \, \text{mol} \]

### Step 2: Determine the number of moles of \( \text{Na}^+ \) ions

Each molecule of \( \text{Na}_3\text{PO}_4 \) dissociates into 3 sodium ions (\( \text{Na}^+ \)). Therefore, to find the number of moles of \( \text{Na}^+ \) ions, we multiply the number of moles of \( \text{Na}_3\text{PO}_4 \) by 3:

\[ \text{Number of moles of } \text{Na}^+ = 3 \times \text{Number of moles of } \text{Na}_3\text{PO}_4 \]

Substituting the value we calculated:

\[ \text{Number of moles of } \text{Na}^+ = 3 \times 0.008 \, \text{mol} = 0.024 \, \text{mol} \]

### Final Answer

Thus, the number of moles of \( \text{Na}^+ \) ions in 20 mL of 0.40 M \( \text{Na}_3\text{PO}_4 \) is **0.024 moles**.

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