To determine the mass of sodium carbonate (Na2CO3) dissolved in a given solution, follow these steps:
1. Identify the molarity of the solution:
The molarity of the Na2CO3 solution is given as 0.724 M (moles per liter).
2. Determine the volume of the solution:
The volume of the solution is 1.421 liters.
3. Calculate the number of moles of Na2CO3:
Use the formula:
[tex]\[
\text{moles of Na2CO3} = \text{molarity} \times \text{volume}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of Na2CO3} = 0.724 \, \text{M} \times 1.421 \, \text{L}
\][/tex]
4. Calculate the molar mass of Na2CO3:
The molar mass of Na2CO3 is calculated by summing the atomic masses of its constituent elements:
[tex]\[
\text{Molar mass of Na2CO3} = 2 \times \text{Na} + 1 \times \text{C} + 3 \times \text{O}
\][/tex]
Using the atomic masses from the periodic table:
[tex]\[
\text{Na} = 22.99 \, \text{g/mol}, \quad \text{C} = 12.01 \, \text{g/mol}, \quad \text{O} = 16.00 \, \text{g/mol}
\][/tex]
Substituting these values:
[tex]\[
\text{Molar mass of Na2CO3} = 2 \times 22.99 + 12.01 + 3 \times 16.00 = 105.99 \, \text{g/mol}
\][/tex]
5. Calculate the mass of Na2CO3:
Use the formula:
[tex]\[
\text{mass of Na2CO3} = \text{moles of Na2CO3} \times \text{molar mass of Na2CO3}
\][/tex]
Substituting the calculated number of moles and the molar mass:
[tex]\[
\text{mass of Na2CO3} = (\text{0.724 M} \times \text{1.421 L}) \times \text{105.99 g/mol}
\][/tex]
6. Express the mass to three significant figures:
The mass of dissolved sodium carbonate is:
[tex]\[
\text{109.043 grams}
\][/tex]
Therefore, the mass of dissolved sodium carbonate is 109.043 grams.
