Determine the percentage composition (by mass) of mixture of anhydrous sodium carbonate and sodium bicarbonate from the following datam:
wt. of the mixture taken = 2g
Loss in weight on heating = 0.124 gm.
Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.

Answer

To determine the percentage composition by mass of a mixture of anhydrous sodium carbonate (Na2CO3) and sodium bicarbonate (NaHCO3), we will follow these steps:

### Step 1: Understand the Reaction
When sodium bicarbonate is heated, it decomposes into sodium carbonate, carbon dioxide, and water:
\[ 2 \text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{CO}_2 + \text{H}_2\text{O} \]
From this reaction, we can see that 2 moles of sodium bicarbonate produce 1 mole of sodium carbonate, 1 mole of carbon dioxide, and 1 mole of water.

### Step 2: Calculate the Molar Masses
- Molar mass of NaHCO3 = 23 (Na) + 1 (H) + 12 (C) + 3*16 (O) = 84 g/mol
- Molar mass of Na2CO3 = 2*23 (Na) + 12 (C) + 3*16 (O) = 106 g/mol
- Molar mass of CO2 = 44 g/mol
- Molar mass of H2O = 18 g/mol

### Step 3: Determine the Mass Loss
The total mass loss during the heating of the mixture is given as 0.124 g. This mass loss corresponds to the mass of the gases (CO2 and H2O) released from the decomposition of sodium bicarbonate.

### Step 4: Set Up the Proportion
From the stoichiometry of the reaction:
- 2 moles of NaHCO3 (168 g) produce 62 g of gases (44 g of CO2 + 18 g of H2O).

Using this ratio, we can find the mass of sodium bicarbonate in the mixture that corresponds to the 0.124 g loss:
\[ \text{Mass of NaHCO}_3 = \frac{168 \, \text{g}}{62 \, \text{g}} \times 0.124 \, \text{g} = 0.336 \, \text{g} \]

### Step 5: Calculate the Mass of Sodium Carbonate
The total mass of the mixture is 2 g. Therefore, the mass of sodium carbonate can be calculated as:
\[ \text{Mass of Na}_2\text{CO}_3 = 2 \, \text{g} - 0.336 \, \text{g} = 1.664 \, \text{g} \]

### Step 6: Calculate the Percentage Composition
Now we can calculate the percentage composition of both sodium bicarbonate and sodium carbonate in the mixture.

**Percentage of Sodium Bicarbonate:**
\[ \text{Percentage of NaHCO}_3 = \left( \frac{0.336 \, \text{g}}{2 \, \text{g}} \right) \times 100 = 16.8\% \]

**Percentage of Sodium Carbonate:**
\[ \text{Percentage of Na}_2\text{CO}_3 = \left( \frac{1.664 \, \text{g}}{2 \, \text{g}} \right) \times 100 = 83.2\% \]

### Final Answer
The percentage composition of the mixture is:
- Sodium Bicarbonate: 16.8%
- Sodium Carbonate: 83.2%

To find the sum of the digits (excluding decimal places) until we get a single digit:
1. For 16.8, sum of digits = 1 + 6 + 8 = 15 → 1 + 5 = 6
2. For 83.2, sum of digits = 8 + 3 + 2 = 13 → 1 + 3 = 4