To determine the molar concentration (in moles per liter, or M) of a solution made with 53.00 grams of [tex]\( \text{Mg(NO}_3\text{)}_2 \)[/tex] dissolved in enough water to make 3.00 liters of solution, we can follow these steps:
1. Calculate the molar mass of [tex]\( \text{Mg(NO}_3\text{)}_2 \)[/tex]:
The molar mass of a compound is found by summing the molar masses of all the atoms in the compound.
- The molar mass of magnesium (Mg) is 24.305 g/mol.
- The molar mass of nitrogen (N) is 14.007 g/mol, and there are 2 nitrogen atoms in the compound.
- The molar mass of oxygen (O) is 15.999 g/mol, and there are 6 oxygen atoms in the compound.
Adding these together:
[tex]\[
\text{Molar mass of } \text{Mg(NO}_3\text{)}_2 = 24.305 \text{ g/mol} + 2 \times 14.007 \text{ g/mol} + 6 \times 15.999 \text{ g/mol}
\][/tex]
[tex]\[
= 24.305 \text{ g/mol} + 28.014 \text{ g/mol} + 95.994 \text{ g/mol}
\][/tex]
[tex]\[
= 148.313 \text{ g/mol}
\][/tex]
2. Calculate the number of moles of [tex]\( \text{Mg(NO}_3\text{)}_2 \)[/tex]:
The number of moles is given by the mass of the substance divided by its molar mass.
[tex]\[
\text{Number of moles} = \frac{\text{Mass of } \text{Mg(NO}_3\text{)}_2}{\text{Molar mass of } \text{Mg(NO}_3\text{)}_2}
\][/tex]
[tex]\[
= \frac{53.00 \text{ g}}{148.313 \text{ g/mol}}
\][/tex]
[tex]\[
= 0.357352 \text{ moles}
\][/tex]
3. Calculate the molar concentration:
The molar concentration is the number of moles of solute divided by the volume of the solution in liters.
[tex]\[
\text{Molar concentration} = \frac{\text{Number of moles of } \text{Mg(NO}_3\text{)}_2}{\text{Volume of solution (in L)}}
\][/tex]
[tex]\[
= \frac{0.357352 \text{ moles}}{3.00 \text{ L}}
\][/tex]
[tex]\[
= 0.119 \text{ M}
\][/tex]
Thus, the molar concentration of the solution is [tex]\( \boxed{0.119 \text{ M}} \)[/tex].
