Answer :
To solve this problem, the goal is to prepare 2.00 liters of a 0.100 M sodium carbonate (Na₂CO₃) solution. We need to determine the correct amount of Na₂CO₃ to weigh and the procedure to follow.
1. Understand the Formula for Molarity:
- Molarity (M) is defined as moles of solute per liter of solution.
- We have a solution with:
[tex]\[ \text{Molarity} = 0.100 \, \text{M} \][/tex]
[tex]\[ \text{Volume} = 2.00 \, \text{L} \][/tex]
2. Calculate Moles of Na₂CO₃ Needed:
- Use the formula for molarity:
[tex]\[ \text{Moles of Na₂CO₃} = \text{Molarity} \times \text{Volume} \][/tex]
- Substituting in the values:
[tex]\[ \text{Moles of Na₂CO₃} = 0.100 \, \text{M} \times 2.00 \, \text{L} = 0.200 \, \text{moles} \][/tex]
3. Determine the Mass of Na₂CO₃ Needed:
- Find the molar mass of Na₂CO₃:
- Sodium (Na) = 22.99 g/mol, Carbon (C) = 12.01 g/mol, Oxygen (O) = 16.00 g/mol
- [tex]\[ \text{Molar Mass of Na₂CO₃} = 2(22.99) + 12.01 + 3(16.00) = 105.99 \, \text{g/mol} \][/tex]
- Calculate the mass using the moles and the molar mass:
[tex]\[ \text{Mass of Na₂CO₃} = 0.200 \, \text{moles} \times 105.99 \, \text{g/mol} = 21.2 \, \text{g} \][/tex]
4. Select the Correct Procedure:
- Based on the calculation, 21.2 g of Na₂CO₃ is required.
- To make sure the final solution is exactly 2.00 liters, we should add water until the total volume reaches 2.00 liters after dissolving 21.2 g of Na₂CO₃.
5. Choose the Correct Option:
- The correct procedure is: Weigh out 21.2 g of Na₂CO₃ and add water until the final solution has a volume of 2.00 L.
This method ensures that the solution's concentration is accurate and matches the desired molarity.
1. Understand the Formula for Molarity:
- Molarity (M) is defined as moles of solute per liter of solution.
- We have a solution with:
[tex]\[ \text{Molarity} = 0.100 \, \text{M} \][/tex]
[tex]\[ \text{Volume} = 2.00 \, \text{L} \][/tex]
2. Calculate Moles of Na₂CO₃ Needed:
- Use the formula for molarity:
[tex]\[ \text{Moles of Na₂CO₃} = \text{Molarity} \times \text{Volume} \][/tex]
- Substituting in the values:
[tex]\[ \text{Moles of Na₂CO₃} = 0.100 \, \text{M} \times 2.00 \, \text{L} = 0.200 \, \text{moles} \][/tex]
3. Determine the Mass of Na₂CO₃ Needed:
- Find the molar mass of Na₂CO₃:
- Sodium (Na) = 22.99 g/mol, Carbon (C) = 12.01 g/mol, Oxygen (O) = 16.00 g/mol
- [tex]\[ \text{Molar Mass of Na₂CO₃} = 2(22.99) + 12.01 + 3(16.00) = 105.99 \, \text{g/mol} \][/tex]
- Calculate the mass using the moles and the molar mass:
[tex]\[ \text{Mass of Na₂CO₃} = 0.200 \, \text{moles} \times 105.99 \, \text{g/mol} = 21.2 \, \text{g} \][/tex]
4. Select the Correct Procedure:
- Based on the calculation, 21.2 g of Na₂CO₃ is required.
- To make sure the final solution is exactly 2.00 liters, we should add water until the total volume reaches 2.00 liters after dissolving 21.2 g of Na₂CO₃.
5. Choose the Correct Option:
- The correct procedure is: Weigh out 21.2 g of Na₂CO₃ and add water until the final solution has a volume of 2.00 L.
This method ensures that the solution's concentration is accurate and matches the desired molarity.
