To find the molarity of the solution, follow these steps:
1. Convert the volume from milliliters to liters:
- We know that 1,000 milliliters is equivalent to 1 liter.
- So, the volume of the solution in liters is:
[tex]\[
\frac{2300 \text{ milliliters}}{1000} = 2.3 \text{ liters}
\][/tex]
2. Determine the molar mass of calcium nitrate [tex]\(\text{Ca(NO}_3\text{)}_2\)[/tex]:
- The atomic masses of the elements are:
- Calcium (Ca): [tex]\(40.08 \text{ g/mol}\)[/tex]
- Nitrogen (N): [tex]\(14.01 \text{ g/mol}\)[/tex] per atom
- Oxygen (O): [tex]\(16.00 \text{ g/mol}\)[/tex] per atom
- Calcium nitrate contains:
- 1 calcium atom
- 2 nitrogen atoms
- 6 oxygen atoms
- Therefore, the molar mass is calculated as:
[tex]\[
40.08 + (2 \times 14.01) + (6 \times 16.00) = 40.08 + 28.02 + 96.00 = 164.1 \text{ g/mol}
\][/tex]
3. Calculate the number of moles of calcium nitrate:
- Using the formula:
[tex]\[
\text{moles} = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
- For the given mass of 127 grams:
[tex]\[
\text{moles} = \frac{127 \text{ grams}}{164.1 \text{ g/mol}} = 0.7739183424741012 \text{ moles}
\][/tex]
4. Determine the molarity of the solution:
- Molarity is defined as the number of moles of solute per liter of solution:
[tex]\[
\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
- Substituting the values:
[tex]\[
\text{Molarity} = \frac{0.7739183424741012 \text{ moles}}{2.3 \text{ liters}} = 0.33605841 \text{ M}
\][/tex]
5. Round the final answer to two significant figures:
[tex]\[
\text{Molarity} \approx 0.34 \text{ M}
\][/tex]
The molarity of the solution is [tex]\(0.34\)[/tex] M.
