`10 g` mixture of `NaHCO_(3)` and `Na_(2)CO_(3)` has `1.68 g NaHCO_(3)`.
It is heated at `400 K`. Weight of the residue will be

Options

A. `9.38 g`
B. `8.32 g`
C. `10.0 g`
D. `1.68 g`

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Identify the components of the mixture
We have a mixture of sodium bicarbonate (NaHCO₃) and sodium carbonate (Na₂CO₃). The total mass of the mixture is 10 g, and the mass of NaHCO₃ is given as 1.68 g.

### Step 2: Calculate the mass of Na₂CO₃ in the mixture
To find the mass of Na₂CO₃, we subtract the mass of NaHCO₃ from the total mass of the mixture:
\[ \text{Mass of Na₂CO₃} = \text{Total mass} - \text{Mass of NaHCO₃} = 10 \, \text{g} - 1.68 \, \text{g} = 8.32 \, \text{g} \]

### Step 3: Write the decomposition reaction of NaHCO₃
When sodium bicarbonate is heated, it decomposes according to the following reaction:
\[ 2 \, \text{NaHCO}_3 \, (s) \rightarrow \text{Na}_2\text{CO}_3 \, (s) + \text{CO}_2 \, (g) + \text{H}_2\text{O} \, (g) \]

### Step 4: Calculate the molar mass of NaHCO₃
The molar mass of NaHCO₃ is:
- Na: 23 g/mol
- H: 1 g/mol
- C: 12 g/mol
- O₃: 16 g/mol × 3 = 48 g/mol
\[ \text{Molar mass of NaHCO}_3 = 23 + 1 + 12 + 48 = 84 \, \text{g/mol} \]

### Step 5: Calculate the amount of NaHCO₃ that decomposes
From the balanced equation, 2 moles of NaHCO₃ produce 1 mole of CO₂ and 1 mole of H₂O. Therefore, the mass loss can be calculated as follows:
- For 2 moles of NaHCO₃ (168 g), the mass loss is the sum of the masses of CO₂ and H₂O produced:
\[ \text{Mass loss} = \text{mass of CO}_2 + \text{mass of H}_2\text{O} = 44 \, \text{g} + 18 \, \text{g} = 62 \, \text{g} \]
Thus, for 1.68 g of NaHCO₃:
\[ \text{Mass loss} = \frac{62 \, \text{g}}{168 \, \text{g}} \times 1.68 \, \text{g} = 0.62 \, \text{g} \]

### Step 6: Calculate the weight of the residue
The weight of the residue after heating can be calculated by subtracting the mass loss from the initial mass of the mixture:
\[ \text{Weight of residue} = \text{Total mass} - \text{Mass loss} = 10 \, \text{g} - 0.62 \, \text{g} = 9.38 \, \text{g} \]

### Final Answer
The weight of the residue will be **9.38 g**.

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