20 g mixture of `Na_(2)CO_(3)` and `CaCO_(3)` is gently heated. On heating this sample produces 2.24 litre of `CO_(2)` at STP. Calculate the % weight of `Na_(2)CO_(3)` in that sample.

Explanation

To solve the problem, we need to determine the percentage weight of \( \text{Na}_2\text{CO}_3 \) in a 20 g mixture of \( \text{Na}_2\text{CO}_3 \) and \( \text{CaCO}_3 \) that produces 2.24 liters of \( \text{CO}_2 \) when heated.

### Step-by-Step Solution:

1. **Define Variables:**
Let the mass of \( \text{Na}_2\text{CO}_3 \) in the mixture be \( x \) grams. Therefore, the mass of \( \text{CaCO}_3 \) will be \( 20 - x \) grams, since the total mass of the mixture is 20 g.

2. **Molar Mass Calculation:**
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