An environment chemist needs a carbonate buffer of `pH=10` to study the effects of the acidification of limestones rich solis.How many grams of `Na_(2)CO_(3)` must be added to `1.5L` of freshly prepared `0.2M NaHCO_(3)` to make the buffer.? For `H_(2)CO_(3),K_(a_(1))=4.7xx10^(-7),K_(a_(2))=4.7xx10^(-11)`

Explanation

To solve the problem of how many grams of \( \text{Na}_2\text{CO}_3 \) must be added to 1.5 L of freshly prepared 0.2 M \( \text{NaHCO}_3 \) to create a buffer with a pH of 10, we can follow these steps:

### Step 1: Understand the Buffer System
The buffer system we are dealing with is based on the equilibrium between \( \text{HCO}_3^- \) (bicarbonate) and \( \text{CO}_3^{2-} \) (carbonate). The relevant dissociation constants are:
- \( K_{a1} \) for \( \text{H}_2\text{CO}_3 \) to \( \text{H}^+ \) and \( \text{HCO}_3^- \): \( K_{a1} = 4.7 \times 10^{-7} \)
- \( K_{a2} \) for \( \text{HCO}_3^- \) to \( \text{H}^+ \) and \( \text{CO}_3^{2-} \): \( K_{a2} = 4.7 \times 10^{-11} \)

### Step 2: Calculate the Concentration of \( \text{H}^+ \)
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