The number of sodium ions in 53g of `Na_(2)CO_(3)` is `x xx 10^(23)`. The value of x is `"______________"`.
( Atomic masses `:` Na = 23u, C = 12u, O = 16u)

Explanation

To solve the problem of finding the number of sodium ions in 53 g of \( \text{Na}_2\text{CO}_3 \), we will follow these steps:

### Step 1: Calculate the Molar Mass of \( \text{Na}_2\text{CO}_3 \)

The molar mass of \( \text{Na}_2\text{CO}_3 \) can be calculated by adding the atomic masses of its constituent elements:

- Sodium (Na): 23 u (2 atoms) = \( 23 \times 2 = 46 \) u
- Carbon (C): 12 u (1 atom) = \( 12 \times 1 = 12 \) u
- Oxygen (O): 16 u (3 atoms) = \( 16 \times 3 = 48 \) u

Now, add these together:

\[ \text{Molar mass of } \text{Na}_2\text{CO}_3 = 46 + 12 + 48 = 106 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of \( \text{Na}_2\text{CO}_3 \)

Using the formula for moles:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{53 \text{ g}}{106 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Determine the Number of Sodium Ions

Each mole of \( \text{Na}_2\text{CO}_3 \) contains 2 moles of sodium ions. Therefore, the total number of moles of sodium ions in 0.5 moles of \( \text{Na}_2\text{CO}_3 \) is:

\[ \text{Moles of sodium ions} = 2 \times 0.5 = 1 \text{ mole} \]

### Step 4: Calculate the Number of Sodium Ions

Using Avogadro's number, which is \( 6.022 \times 10^{23} \) ions/mole, we can find the total number of sodium ions:

\[ \text{Number of sodium ions} = 1 \text{ mole} \times 6.022 \times 10^{23} \text{ ions/mole} = 6.022 \times 10^{23} \text{ ions} \]

### Step 5: Identify the Value of \( x \)

From the calculation, we see that the number of sodium ions is \( 6.022 \times 10^{23} \). Therefore, the value of \( x \) is:

\[ x = 6.022 \]

### Final Answer

The value of \( x \) is **6.022**.

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