To determine the amount concentration (molarity) of magnesium chloride ([tex]\( \text{MgCl}_2 \)[/tex]) dissolved in a 45 mL solution, follow these steps:
1. Given Data:
- Mass of [tex]\( \text{MgCl}_2 \)[/tex]: [tex]\( 2.6 \times 10^{-2} \)[/tex] grams
- Volume of the solution: 45 mL
2. Calculate the molar mass of [tex]\( \text{MgCl}_2 \)[/tex]:
- The molar mass of magnesium (Mg) is approximately [tex]\( 24.305 \)[/tex] g/mol.
- The molar mass of chlorine (Cl) is approximately [tex]\( 35.453 \)[/tex] g/mol.
- Since there are two chlorine atoms in [tex]\( \text{MgCl}_2 \)[/tex], we calculate the molar mass as follows:
[tex]\[
\text{Molar mass of } \text{MgCl}_2 = 24.305 + 2 \times 35.453 = 95.211 \text{ g/mol}
\][/tex]
3. Convert the volume of the solution from mL to L:
- 1 L = 1000 mL
- Therefore, the volume of the solution in liters is:
[tex]\[
\text{Volume of solution} = \frac{45 \text{ mL}}{1000} = 0.045 \text{ L}
\][/tex]
4. Calculate the number of moles of [tex]\( \text{MgCl}_2 \)[/tex]:
- The number of moles ([tex]\( n \)[/tex]) is given by:
[tex]\[
\text{moles of } \text{MgCl}_2 = \frac{\text{mass of } \text{MgCl}_2}{\text{molar mass of } \text{MgCl}_2}
\][/tex]
- Substituting the given values:
[tex]\[
\text{moles of } \text{MgCl}_2 = \frac{2.6 \times 10^{-2} \text{ g}}{95.211 \text{ g/mol}} \approx 0.00027308 \text{ moles}
\][/tex]
5. Calculate the molarity (amount concentration) of [tex]\( \text{MgCl}_2 \)[/tex]:
- Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters:
[tex]\[
\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
- Substituting the values into the formula:
[tex]\[
\text{Molarity of } \text{MgCl}_2 = \frac{0.00027308 \text{ moles}}{0.045 \text{ L}} \approx 0.006068 \text{ M}
\][/tex]
Final Result:
- The amount concentration (molarity) of [tex]\( 2.6 \times 10^{-2} \)[/tex] grams of magnesium chloride dissolved in 45 mL of solution is approximately [tex]\( 0.006068 \)[/tex] M.
